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skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Vectorveld rootpage-Vectorveld skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Naar inhoud springen</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Hoofdmenu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Hoofdmenu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Hoofdmenu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">verbergen</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Hoofdpagina" title="Naar de hoofdpagina gaan [z]" accesskey="z"><span>Hoofdpagina</span></a></li><li id="n-zoekartikel" class="mw-list-item"><a href="/wiki/Portaal:Navigatie"><span>Vind een artikel</span></a></li><li id="n-today" class="mw-list-item"><a href="/wiki/12_december"><span>Vandaag</span></a></li><li id="n-Etalage" class="mw-list-item"><a href="/wiki/Wikipedia:Etalage"><span>Etalage</span></a></li><li id="n-categories" class="mw-list-item"><a href="/wiki/Categorie:Alles"><span>Categorieën</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingen" title="Een lijst met recente wijzigingen in deze wiki. [r]" accesskey="r"><span>Recente wijzigingen</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/Speciaal:NieuwePaginas"><span>Nieuwe artikelen</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speciaal:Willekeurig" title="Een willekeurige pagina bekijken [x]" accesskey="x"><span>Willekeurige pagina</span></a></li> </ul> </div> </div> <div id="p-navigation2" class="vector-menu mw-portlet mw-portlet-navigation2" > <div class="vector-menu-heading"> Informatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Portaal:Gebruikersportaal" title="Informatie over het project: wat u kunt doen, waar u dingen kunt vinden"><span>Gebruikersportaal</span></a></li><li id="n-Snelcursus" class="mw-list-item"><a href="/wiki/Wikipedia:Snelcursus"><span>Snelcursus</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Portaal:Hulp_en_beheer" title="Hulpinformatie over deze wiki"><span>Hulp en contact</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hoofdpagina" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="de vrije encyclopedie" src="/static/images/mobile/copyright/wikipedia-tagline-nl.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Speciaal:Zoeken" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Doorzoek Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Zoeken</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Doorzoek Wikipedia" aria-label="Doorzoek Wikipedia" autocapitalize="sentences" title="Doorzoek Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Speciaal:Zoeken"> </div> <button class="cdx-button cdx-search-input__end-button">Zoeken</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Persoonlijke hulpmiddelen"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="De lettergrootte, breedte en kleur van de pagina wijzigen" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Uiterlijk" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Uiterlijk</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=nl.wikipedia.org&uselang=nl" class=""><span>Doneren</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciaal:GebruikerAanmaken&returnto=Vectorveld" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht." class=""><span>Account aanmaken</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciaal:Aanmelden&returnto=Vectorveld" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o" class=""><span>Aanmelden</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Meer opties" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Persoonlijke hulpmiddelen" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Persoonlijke hulpmiddelen</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Gebruikersmenu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=nl.wikipedia.org&uselang=nl"><span>Doneren</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:GebruikerAanmaken&returnto=Vectorveld" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Account aanmaken</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:Aanmelden&returnto=Vectorveld" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Aanmelden</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pagina's voor uitgelogde redacteuren <a href="/wiki/Help:Inleiding" aria-label="Meer leren over bewerken"><span>meer lezen</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciaal:MijnBijdragen" title="Bijdragen IP-adres [y]" accesskey="y"><span>Bijdragen</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciaal:MijnOverleg" title="Overlegpagina van de anonieme gebruiker van dit IP-adres [n]" accesskey="n"><span>Overleg</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Inhoud" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">verbergen</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Top</div> </a> </li> <li id="toc-Definitie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definitie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definitie</span> </div> </a> <ul id="toc-Definitie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voorbeelden" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voorbeelden"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Voorbeelden</span> </div> </a> <button aria-controls="toc-Voorbeelden-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Voorbeelden-subkopje inklappen</span> </button> <ul id="toc-Voorbeelden-sublist" class="vector-toc-list"> <li id="toc-Windrichting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Windrichting"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Windrichting</span> </div> </a> <ul id="toc-Windrichting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zwaartekracht" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zwaartekracht"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Zwaartekracht</span> </div> </a> <ul id="toc-Zwaartekracht-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bewerkingen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bewerkingen"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Bewerkingen</span> </div> </a> <button aria-controls="toc-Bewerkingen-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Bewerkingen-subkopje inklappen</span> </button> <ul id="toc-Bewerkingen-sublist" class="vector-toc-list"> <li id="toc-Integreren" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Integreren"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Integreren</span> </div> </a> <ul id="toc-Integreren-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differentiëren" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differentiëren"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Differentiëren</span> </div> </a> <ul id="toc-Differentiëren-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gekromde_ruimten" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gekromde_ruimten"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Gekromde ruimten</span> </div> </a> <ul id="toc-Gekromde_ruimten-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Inhoud" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Inhoudsopgave omschakelen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Inhoudsopgave omschakelen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Vectorveld</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ga naar een artikel in een andere taal. Beschikbaar in 54 talen" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-54" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">54 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Vektorveld" title="Vektorveld – Afrikaans" lang="af" hreflang="af" data-title="Vektorveld" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D9%82%D9%84_%D9%85%D8%AA%D8%AC%D9%87%D8%A7%D8%AA" title="حقل متجهات – Arabisch" lang="ar" hreflang="ar" data-title="حقل متجهات" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D0%B5_%D0%BF%D0%BE%D0%BB%D0%B5" title="Вектарнае поле – Belarussisch" lang="be" hreflang="be" data-title="Вектарнае поле" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%BE_%D0%BF%D0%BE%D0%BB%D0%B5" title="Векторно поле – Bulgaars" lang="bg" hreflang="bg" data-title="Векторно поле" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Vektorsko_polje" title="Vektorsko polje – Bosnisch" lang="bs" hreflang="bs" data-title="Vektorsko polje" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Camp_vectorial" title="Camp vectorial – Catalaans" lang="ca" hreflang="ca" data-title="Camp vectorial" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vektorov%C3%A9_pole" title="Vektorové pole – Tsjechisch" lang="cs" hreflang="cs" data-title="Vektorové pole" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BB%C4%83_%D1%83%D0%B9" title="Векторлă уй – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Векторлă уй" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Vektorfeld" title="Vektorfeld – Duits" lang="de" hreflang="de" data-title="Vektorfeld" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Vector_field" title="Vector field – Engels" lang="en" hreflang="en" data-title="Vector field" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Vektora_kampo" title="Vektora kampo – Esperanto" lang="eo" hreflang="eo" data-title="Vektora kampo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Campo_vectorial" title="Campo vectorial – Spaans" lang="es" hreflang="es" data-title="Campo vectorial" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Vektorv%C3%A4li" title="Vektorväli – Estisch" lang="et" hreflang="et" data-title="Vektorväli" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bektore-eremua" title="Bektore-eremua – Baskisch" lang="eu" hreflang="eu" data-title="Bektore-eremua" data-language-autonym="Euskara" data-language-local-name="Baskisch" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DB%8C%D8%AF%D8%A7%D9%86_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1%DB%8C" title="میدان برداری – Perzisch" lang="fa" hreflang="fa" data-title="میدان برداری" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vektorikentt%C3%A4" title="Vektorikenttä – Fins" lang="fi" hreflang="fi" data-title="Vektorikenttä" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Champ_de_vecteurs" title="Champ de vecteurs – Frans" lang="fr" hreflang="fr" data-title="Champ de vecteurs" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Campo_vectorial" title="Campo vectorial – Galicisch" lang="gl" hreflang="gl" data-title="Campo vectorial" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%93%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="שדה וקטורי – Hebreeuws" lang="he" hreflang="he" data-title="שדה וקטורי" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%A6%E0%A4%BF%E0%A4%B6_%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="सदिश क्षेत्र – Hindi" lang="hi" hreflang="hi" data-title="सदिश क्षेत्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Vektorsko_polje" title="Vektorsko polje – Kroatisch" lang="hr" hreflang="hr" data-title="Vektorsko polje" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Chan_vektory%C3%A8l" title="Chan vektoryèl – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Chan vektoryèl" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Vektormez%C5%91" title="Vektormező – Hongaars" lang="hu" hreflang="hu" data-title="Vektormező" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8E%D5%A5%D5%AF%D5%BF%D5%B8%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A4%D5%A1%D5%B7%D5%BF" title="Վեկտորական դաշտ – Armeens" lang="hy" hreflang="hy" data-title="Վեկտորական դաշտ" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Vektorofeldo" title="Vektorofeldo – Ido" lang="io" hreflang="io" data-title="Vektorofeldo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Vigursvi%C3%B0" title="Vigursvið – IJslands" lang="is" hreflang="is" data-title="Vigursvið" data-language-autonym="Íslenska" data-language-local-name="IJslands" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Campo_vettoriale" title="Campo vettoriale – Italiaans" lang="it" hreflang="it" data-title="Campo vettoriale" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E5%A0%B4" title="ベクトル場 – Japans" lang="ja" hreflang="ja" data-title="ベクトル場" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BB%D1%8B%D2%9B_%D3%A9%D1%80%D1%96%D1%81" title="Векторлық өріс – Kazachs" lang="kk" hreflang="kk" data-title="Векторлық өріс" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B2%A1%ED%84%B0%EC%9E%A5" title="벡터장 – Koreaans" lang="ko" hreflang="ko" data-title="벡터장" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B4%D1%83%D0%BA_%D1%82%D0%B0%D0%BB%D0%B0%D0%B0" title="Вектордук талаа – Kirgizisch" lang="ky" hreflang="ky" data-title="Вектордук талаа" data-language-autonym="Кыргызча" data-language-local-name="Kirgizisch" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vektorinis_laukas" title="Vektorinis laukas – Litouws" lang="lt" hreflang="lt" data-title="Vektorinis laukas" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D0%BE%D1%80%D0%BE%D0%BD" title="Вектор орон – Mongools" lang="mn" hreflang="mn" data-title="Вектор орон" data-language-autonym="Монгол" data-language-local-name="Mongools" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Vektorfelt" title="Vektorfelt – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Vektorfelt" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Vektorfelt" title="Vektorfelt – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Vektorfelt" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%88%E0%A8%95%E0%A8%9F%E0%A8%B0_%E0%A8%AB%E0%A9%80%E0%A8%B2%E0%A8%A1" title="ਵੈਕਟਰ ਫੀਲਡ – Punjabi" lang="pa" hreflang="pa" data-title="ਵੈਕਟਰ ਫੀਲਡ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pole_wektorowe" title="Pole wektorowe – Pools" lang="pl" hreflang="pl" data-title="Pole wektorowe" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%DB%8C%DA%A9%D9%B9%D8%B1_%D9%81%DB%8C%D9%84%DA%88" title="ویکٹر فیلڈ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ویکٹر فیلڈ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%84%D9%88%D8%B1%DB%8C_%D9%85%D9%8A%D8%AF%D8%A7%D9%86" title="لوری ميدان – Pasjtoe" lang="ps" hreflang="ps" data-title="لوری ميدان" data-language-autonym="پښتو" data-language-local-name="Pasjtoe" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Campo_vetorial" title="Campo vetorial – Portugees" lang="pt" hreflang="pt" data-title="Campo vetorial" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/C%C3%A2mp_vectorial" title="Câmp vectorial – Roemeens" lang="ro" hreflang="ro" data-title="Câmp vectorial" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%BE%D0%B5_%D0%BF%D0%BE%D0%BB%D0%B5" title="Векторное поле – Russisch" lang="ru" hreflang="ru" data-title="Векторное поле" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Vektorsko_polje" title="Vektorsko polje – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Vektorsko polje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Vector_field" title="Vector field – Simple English" lang="en-simple" hreflang="en-simple" data-title="Vector field" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Vektorov%C3%A9_pole" title="Vektorové pole – Slowaaks" lang="sk" hreflang="sk" data-title="Vektorové pole" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vektorsko_polje" title="Vektorsko polje – Sloveens" lang="sl" hreflang="sl" data-title="Vektorsko polje" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Fusha_vektoriale" title="Fusha vektoriale – Albanees" lang="sq" hreflang="sq" data-title="Fusha vektoriale" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Vektorf%C3%A4lt" title="Vektorfält – Zweeds" lang="sv" hreflang="sv" data-title="Vektorfält" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Vekt%C3%B6r_alan%C4%B1" title="Vektör alanı – Turks" lang="tr" hreflang="tr" data-title="Vektör alanı" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%B5_%D0%BF%D0%BE%D0%BB%D0%B5" title="Векторне поле – Oekraïens" lang="uk" hreflang="uk" data-title="Векторне поле" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B3%D9%85%D8%AA%DB%8C%DB%81_%D9%85%DB%8C%D8%AF%D8%A7%D9%86" title="سمتیہ میدان – Urdu" lang="ur" hreflang="ur" data-title="سمتیہ میدان" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Vektor_maydon" title="Vektor maydon – Oezbeeks" lang="uz" hreflang="uz" data-title="Vektor maydon" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tr%C6%B0%E1%BB%9Dng_vect%C6%A1" title="Trường vectơ – Vietnamees" lang="vi" hreflang="vi" data-title="Trường vectơ" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%90%91%E9%87%8F%E5%A0%B4" title="向量場 – Chinees" lang="zh" hreflang="zh" data-title="向量場" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q186247#sitelinks-wikipedia" title="Taalkoppelingen bewerken" class="wbc-editpage">Koppelingen bewerken</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Naamruimten"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Vectorveld" title="Inhoudspagina bekijken [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Overleg:Vectorveld&action=edit&redlink=1" rel="discussion" class="new" title="Overleg over deze pagina (de pagina bestaat niet) [t]" accesskey="t"><span>Overleg</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" 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<button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">verbergen</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Meer opties" > <div class="vector-menu-heading"> Handelingen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Vectorveld"><span>Lezen</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vectorveld&veaction=edit" title="Deze pagina bewerken [v]" accesskey="v"><span>Bewerken</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vectorveld&action=edit" title="Broncode van deze pagina bewerken [e]" accesskey="e"><span>Brontekst bewerken</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vectorveld&action=history"><span>Geschiedenis weergeven</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Algemeen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciaal:VerwijzingenNaarHier/Vectorveld" title="Lijst met alle pagina's die naar deze pagina verwijzen [j]" accesskey="j"><span>Links naar deze pagina</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingenGelinkt/Vectorveld" rel="nofollow" title="Recente wijzigingen in pagina's waar deze pagina naar verwijst 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citeren"><span>Deze pagina citeren</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciaal:UrlQ%C4%B1sald%C4%B1c%C4%B1s%C4%B1&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FVectorveld"><span>Verkorte URL verkrijgen</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciaal:QrKodu&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FVectorveld"><span>QR-code downloaden</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Afdrukken/exporteren </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciaal:Boek&bookcmd=book_creator&referer=Vectorveld"><span>Boek aanmaken</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciaal:DownloadAsPdf&page=Vectorveld&action=show-download-screen"><span>Downloaden als PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Vectorveld&printable=yes" title="Printvriendelijke versie van deze pagina [p]" accesskey="p"><span>Afdrukversie</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In andere projecten </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Vector_fields" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q186247" title="Koppeling naar item in verbonden gegevensrepository [g]" accesskey="g"><span>Wikidata-item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Paginahulpmiddelen"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Uiterlijk</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:Vectorfield_jaredwf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Vectorfield_jaredwf.png/320px-Vectorfield_jaredwf.png" decoding="async" width="320" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/88/Vectorfield_jaredwf.png 1.5x" data-file-width="400" data-file-height="356" /></a><figcaption>Voorbeeld van een vectorveld: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [-y,x]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mo>−</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [-y,x]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4af0cda7306576afc564a26b866cb3c93f5e0c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.621ex; height:2.843ex;" alt="{\displaystyle [-y,x]}"></span></figcaption></figure> <p>Een <b>vectorveld</b> is in de <a href="/wiki/Vectoranalyse" title="Vectoranalyse">vectoranalyse</a> een <a href="/wiki/Afbeelding_(wiskunde)" title="Afbeelding (wiskunde)">afbeelding</a> die aan elk punt in een <a href="/wiki/Euclidische_ruimte" title="Euclidische ruimte">euclidische ruimte</a> een <a href="/wiki/Vector_(wiskunde)" title="Vector (wiskunde)">vector</a> toekent. Men spreekt wel van gebonden vectoren met een <a href="/wiki/Aangrijpingspunt" title="Aangrijpingspunt">aangrijpingspunt</a>. </p><p>In de <a href="/wiki/Natuurkunde" title="Natuurkunde">natuurkunde</a> worden vectorvelden bijvoorbeeld gebruikt voor het beschrijven van de <a href="/wiki/Vloeistofmechanica" title="Vloeistofmechanica">stroming van een vloeistof</a> door van elk punt in de stroming de <a href="/wiki/Snelheid" title="Snelheid">snelheid</a> in grootte en richting te geven of van een <a href="/wiki/Magnetisch_veld" title="Magnetisch veld">magnetisch veld</a> of <a href="/wiki/Zwaartekrachtsveld" title="Zwaartekrachtsveld">zwaartekrachtsveld</a> door in elk punt de grootte en de richting waarin de <a href="/wiki/Kracht" title="Kracht">kracht</a> werkt te geven. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definitie">Definitie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=1" title="Bewerk dit kopje: Definitie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=1" title="De broncode bewerken van de sectie: Definitie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een vectorveld <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> is een <a href="/wiki/Afbeelding_(wiskunde)" title="Afbeelding (wiskunde)">afbeelding</a> die aan elk punt van een <a href="/wiki/Vectorruimte" title="Vectorruimte">vectorruimte</a> een <a href="/wiki/Vector_(wiskunde)" title="Vector (wiskunde)">vector</a> uit die ruimte toekent. </p> <ul><li>in de driedimensionale ruimte:</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}(x,y,z)=(F_{x}(x,y,z),F_{y}(x,y,z),F_{z}(x,y,z))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}(x,y,z)=(F_{x}(x,y,z),F_{y}(x,y,z),F_{z}(x,y,z))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74aad62980a41b5bad5a6ca554b1323a0baa8184" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:46.256ex; height:3.509ex;" alt="{\displaystyle {\vec {F}}(x,y,z)=(F_{x}(x,y,z),F_{y}(x,y,z),F_{z}(x,y,z))}"></span></dd></dl></dd></dl> <ul><li>in de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-dimensionale Euclidische ruimte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span>:</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}(x_{1},x_{2},\ldots ,x_{n})=(F_{1}(x_{1},\ldots ,x_{n}),F_{2}(x_{1},\ldots ,x_{n}),\ldots ,F_{n}(x_{1},\ldots ,x_{n}))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}(x_{1},x_{2},\ldots ,x_{n})=(F_{1}(x_{1},\ldots ,x_{n}),F_{2}(x_{1},\ldots ,x_{n}),\ldots ,F_{n}(x_{1},\ldots ,x_{n}))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d34cd7909ce745d5346f49a231ebc533e4f12f03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:71.798ex; height:3.343ex;" alt="{\displaystyle {\vec {F}}(x_{1},x_{2},\ldots ,x_{n})=(F_{1}(x_{1},\ldots ,x_{n}),F_{2}(x_{1},\ldots ,x_{n}),\ldots ,F_{n}(x_{1},\ldots ,x_{n}))}"></span>.</dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Voorbeelden">Voorbeelden</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=2" title="Bewerk dit kopje: Voorbeelden" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=2" title="De broncode bewerken van de sectie: Voorbeelden"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Windrichting">Windrichting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=3" title="Bewerk dit kopje: Windrichting" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=3" title="De broncode bewerken van de sectie: Windrichting"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bekijken we de verdeling van de <a href="/wiki/Windsnelheid" class="mw-redirect" title="Windsnelheid">windsnelheid</a> in de <a href="/wiki/Aardatmosfeer" title="Aardatmosfeer">atmosfeer</a>, dan heerst op ieder punt een bepaalde <a href="/wiki/Windrichting" class="mw-redirect" title="Windrichting">windrichting</a> en windsnelheid. Deze verdeling is dus een vectorveld van aan punten <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22a8c93372e8f8b6e24d523bd5545aed3430baf4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.45ex; height:2.843ex;" alt="{\displaystyle (x,y,z)}"></span> in de atmosfeer gekoppelde snelheidsvectoren </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}(x,y,z)=(v_{x}(x,y,z),v_{y}(x,y,z),v_{z}(x,y,z))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}(x,y,z)=(v_{x}(x,y,z),v_{y}(x,y,z),v_{z}(x,y,z))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d3a65296e7484c6acf6a1a3a652cc727a069906" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:44.559ex; height:3.009ex;" alt="{\displaystyle {\vec {v}}(x,y,z)=(v_{x}(x,y,z),v_{y}(x,y,z),v_{z}(x,y,z))}"></span>.</dd></dl> <p>Waait de wind alleen in één richting, zeg de x-richting, zoals bij <a href="/wiki/Benadering" title="Benadering">benadering</a> in een <a href="/wiki/Windtunnel" title="Windtunnel">windtunnel</a>, dan is het vectorveld van de vorm <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (v_{x},0,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (v_{x},0,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e2ce7b16778c4bb5623118a6dc0c05636a87a62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.502ex; height:2.843ex;" alt="{\displaystyle (v_{x},0,0)}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Zwaartekracht">Zwaartekracht</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=4" title="Bewerk dit kopje: Zwaartekracht" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=4" title="De broncode bewerken van de sectie: Zwaartekracht"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Op ieder <a href="/wiki/Punt_(wiskunde)" title="Punt (wiskunde)">punt</a> van de <a href="/wiki/Ruimte_(wiskunde)" title="Ruimte (wiskunde)">ruimte</a> geldt een bepaald <a href="/wiki/Zwaartekrachtsveld" title="Zwaartekrachtsveld">zwaartekrachtsveld</a>, gegeven door de <a href="/wiki/Richting" title="Richting">richting</a> van de <a href="/wiki/Zwaartekracht" title="Zwaartekracht">zwaartekracht</a>, 'naar beneden', en een grootte, de <a href="/wiki/Veldsterkte" title="Veldsterkte">veldsterkte</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span>. Het vectorveld wordt dan: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {g}}=(0,0,-g)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mo>−</mo> <mi>g</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {g}}=(0,0,-g)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e312567d975c4cf5967dd16454f7cdea1222ef1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.399ex; height:2.843ex;" alt="{\displaystyle {\vec {g}}=(0,0,-g)}"></span>. Alle <a href="/wiki/Kracht" title="Kracht">krachten</a> hebben in de natuurkunde een <a href="/wiki/Veld_(natuurkunde)" title="Veld (natuurkunde)">veld</a>, dat in veel gevallen een vectorveld is. </p> <div class="mw-heading mw-heading2"><h2 id="Bewerkingen">Bewerkingen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=5" title="Bewerk dit kopje: Bewerkingen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=5" title="De broncode bewerken van de sectie: Bewerkingen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Integreren">Integreren</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=6" title="Bewerk dit kopje: Integreren" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=6" title="De broncode bewerken van de sectie: Integreren"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het <a href="/wiki/Integraalrekening" title="Integraalrekening">integreren</a> van een vectorveld wordt gebruikt in de <a href="/wiki/Wetten_van_Maxwell" title="Wetten van Maxwell">wetten van Maxwell</a>, daarbij integreert men over de <a href="/wiki/Inhoud_(volume)" title="Inhoud (volume)">inhoud</a> of over het <a href="/wiki/Vlak_(meetkunde)" title="Vlak (meetkunde)">oppervlak</a> van een gegeven volume. </p> <div class="mw-heading mw-heading3"><h3 id="Differentiëren"><span id="Differenti.C3.ABren"></span>Differentiëren</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=7" title="Bewerk dit kopje: Differentiëren" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=7" title="De broncode bewerken van de sectie: Differentiëren"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Om de verschillende <a href="/wiki/Afgeleide" title="Afgeleide">afgeleiden</a> te beschrijven, maakt men vaak gebruik van de <a href="/wiki/Nabla" title="Nabla">nabla-operator</a>. </p><p>De <a href="/wiki/Richtingsafgeleide" title="Richtingsafgeleide">richtingsafgeleiden</a> van een <a href="/wiki/Scalair_veld" title="Scalair veld">scalair veld</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> vormen een vectorveld, de <a href="/wiki/Gradi%C3%ABnt_(wiskunde)" title="Gradiënt (wiskunde)">gradiënt</a> van het veld: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {grad} \;\phi =\nabla \phi =\left({\frac {\partial \phi }{\partial x}},{\frac {\partial \phi }{\partial y}},{\frac {\partial \phi }{\partial z}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mspace width="thickmathspace" /> <mi>ϕ</mi> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mi>ϕ</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {grad} \;\phi =\nabla \phi =\left({\frac {\partial \phi }{\partial x}},{\frac {\partial \phi }{\partial y}},{\frac {\partial \phi }{\partial z}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e19a53c70f2cf2c00b8b060fd7188eb0d9e9851d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.186ex; height:6.176ex;" alt="{\displaystyle \mathrm {grad} \;\phi =\nabla \phi =\left({\frac {\partial \phi }{\partial x}},{\frac {\partial \phi }{\partial y}},{\frac {\partial \phi }{\partial z}}\right)}"></span></dd></dl> <p>Een dergelijk veld heet een <a href="/wiki/Conservatief_vectorveld" title="Conservatief vectorveld">conservatief vectorveld</a>. </p><p>Om de putten en bronnen van een vectorveld φ aan te geven berekent men de <a href="/wiki/Divergentie_(vectorveld)" title="Divergentie (vectorveld)">divergentie</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c74bd363806e988f7b2a7596164d692a9fc527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5ex; height:2.509ex;" alt="{\displaystyle \nabla \cdot \phi }"></span> van het veld. De divergentie is een <a href="/wiki/Scalair" title="Scalair">scalair</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {div} \;\phi =\nabla \cdot \phi ={\frac {\partial \phi _{x}}{\partial x}}+{\frac {\partial \phi _{y}}{\partial y}}+{\frac {\partial \phi _{z}}{\partial z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">v</mi> </mrow> <mspace width="thickmathspace" /> <mi>ϕ</mi> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {div} \;\phi =\nabla \cdot \phi ={\frac {\partial \phi _{x}}{\partial x}}+{\frac {\partial \phi _{y}}{\partial y}}+{\frac {\partial \phi _{z}}{\partial z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd084cf406f5daa124b1647b1ea67af8d2d307a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.918ex; height:6.343ex;" alt="{\displaystyle \mathrm {div} \;\phi =\nabla \cdot \phi ={\frac {\partial \phi _{x}}{\partial x}}+{\frac {\partial \phi _{y}}{\partial y}}+{\frac {\partial \phi _{z}}{\partial z}}}"></span></dd></dl> <p>Of een veld wervelingen kent, wordt bepaald door de <a href="/wiki/Rotatie_(vectorveld)" title="Rotatie (vectorveld)">rotatie</a> of rotor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/516a972905d45bbdf80ea8a0ec74818a5faa4b35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.162ex; height:2.509ex;" alt="{\displaystyle \nabla \times \phi }"></span> van het veld: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {rot} \;\phi =\nabla \times \phi =\left({\frac {\partial \phi _{z}}{\partial y}}-{\frac {\partial \phi _{y}}{\partial z}},{\frac {\partial \phi _{x}}{\partial z}}-{\frac {\partial \phi _{z}}{\partial x}},{\frac {\partial \phi _{y}}{\partial x}}-{\frac {\partial \phi _{x}}{\partial y}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> </mrow> <mspace width="thickmathspace" /> <mi>ϕ</mi> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mi>ϕ</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {rot} \;\phi =\nabla \times \phi =\left({\frac {\partial \phi _{z}}{\partial y}}-{\frac {\partial \phi _{y}}{\partial z}},{\frac {\partial \phi _{x}}{\partial z}}-{\frac {\partial \phi _{z}}{\partial x}},{\frac {\partial \phi _{y}}{\partial x}}-{\frac {\partial \phi _{x}}{\partial y}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7db9a7748052fc6ea2cfd3d95b0d22238d8db6c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:59.063ex; height:6.343ex;" alt="{\displaystyle \mathrm {rot} \;\phi =\nabla \times \phi =\left({\frac {\partial \phi _{z}}{\partial y}}-{\frac {\partial \phi _{y}}{\partial z}},{\frac {\partial \phi _{x}}{\partial z}}-{\frac {\partial \phi _{z}}{\partial x}},{\frac {\partial \phi _{y}}{\partial x}}-{\frac {\partial \phi _{x}}{\partial y}}\right)}"></span></dd></dl> <p>Belangrijk op te merken is, dat deze vorm alleen in een <a href="/wiki/Cartesisch_co%C3%B6rdinatenstelsel" title="Cartesisch coördinatenstelsel">cartesiaans coördinatenstelsel</a> geldt, in een ander assenstelsel is de vorm anders. Er zijn regels om de werking van de nabla-operator in verschillende assenstelsels naar elkaar te converteren.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Gekromde_ruimten">Gekromde ruimten</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vectorveld&veaction=edit&section=8" title="Bewerk dit kopje: Gekromde ruimten" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vectorveld&action=edit&section=8" title="De broncode bewerken van de sectie: Gekromde ruimten"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het is ook in willekeurige gekromde ruimten, in <a href="/wiki/Vari%C3%ABteit_(wiskunde)" title="Variëteit (wiskunde)">variëteiten</a>, mogelijk een betekenis aan gebonden vectoren te geven. </p><p>De <a href="/wiki/Differentiaalmeetkunde" title="Differentiaalmeetkunde">differentiaalmeetkunde</a> associeert met elk punt <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> van een gladde variëteit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> een vectorruimte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{p}M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{p}M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71b20e0304a65ead2cafb33412a383b34fe527ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.859ex; height:2.843ex;" alt="{\displaystyle T_{p}M}"></span>, die <a href="/wiki/Raakruimte" title="Raakruimte">raakruimte</a> wordt genoemd. De <a href="/wiki/Vereniging_(verzamelingenleer)" title="Vereniging (verzamelingenleer)">vereniging</a> van alle raakruimten is de <a href="/wiki/Raakbundel" title="Raakbundel">raakbundel</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle TM}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TM}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea000afb5769206ddd5fd43f458430d04422ddeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.078ex; height:2.176ex;" alt="{\displaystyle TM}"></span>, en een vectorveld is een 'sectie' van de raakbundel, dat is een gladde afbeelding van <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> naar <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle TM}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TM}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea000afb5769206ddd5fd43f458430d04422ddeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.078ex; height:2.176ex;" alt="{\displaystyle TM}"></span> die elk punt <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> op een vector in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{p}M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{p}M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71b20e0304a65ead2cafb33412a383b34fe527ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.859ex; height:2.843ex;" alt="{\displaystyle T_{p}M}"></span> afbeeldt. </p><p>De differentiaaloperatoren <a href="/wiki/Gradi%C3%ABnt_(wiskunde)" title="Gradiënt (wiskunde)">gradiënt</a>, <a href="/wiki/Divergentie_(vectorveld)" title="Divergentie (vectorveld)">divergentie</a> en <a href="/wiki/Rotatie_(vectorveld)" title="Rotatie (vectorveld)">rotatie</a> worden <a href="/wiki/Operatie_(wiskunde)" title="Operatie (wiskunde)">bewerkingen</a> in de uitwendige algebra van de <a href="/wiki/Differentiaalvorm" title="Differentiaalvorm">differentiaalvormen</a> van een willekeurige <a href="/wiki/Differentieerbare_vari%C3%ABteit" title="Differentieerbare variëteit">gladde variëteit</a>. Om echter te behouden dat de gradiënt een operatie van scalairen naar vectorvelden is en de divergentie een bewerking van vectorvelden naar scalairen, hebben we de aanvullende structuur van een <a href="/wiki/Metrische_tensor" title="Metrische tensor">metrische tensor</a> nodig; dat wil zeggen dat de gladde variëteit een <a href="/wiki/Riemann-vari%C3%ABteit" title="Riemann-variëteit">riemann-variëteit</a> is. </p><p>De rotatie, zoals hierboven gedefinieerd, heeft betrekking op een driedimensionale oriënteerbare ruimte. In het algemeen, met <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> dimensies en geen oriëntatie, betreft het de operator <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {d} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {d} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e1d5ee1d8ebd36dc6c040835c50f112c7da3e75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="{\displaystyle \operatorname {d} }"></span> in de <a href="/wiki/Tensoralgebra" title="Tensoralgebra">uitwendige algebra</a>. </p><p>Nog algemener kan een vectorveld een sectie zijn van iedere gegeven <a href="/wiki/Vectorbundel" title="Vectorbundel">vectorbundel</a> over de beschouwde ruimte. </p> <div class="interProject commons mw-list-item" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Vector_fields#mw-subcategories" class="extiw" title="commons:Category:Vector fields">Mediabestanden</a></div> <div class="interProjectTemplate interProject-groot toccolours" style="display:flex; gap:1em; align-items:center; clear:both; margin:1em 0 -0.5em 0;"> <div style="min-width:max-content;"><span class="noviewer noresize" typeof="mw:File"><a href="/wiki/Bestand:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/25px-Commons-logo.svg.png" decoding="async" width="25" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/38px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div>Zie de categorie <i><b><a href="https://commons.wikimedia.org/wiki/Category:Vector_fields#mw-subcategories" class="extiw" title="commons:Category:Vector fields">Vector fields</a></b></i> van <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> voor mediabestanden over dit onderwerp.</div> </div> <div class="toccolours appendix" role="presentation" style="font-size:90%; 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