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Vlak - Wikipedia

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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">Hoofkieslys</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">versteek</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigasie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Tuisblad" title="Besoek die Tuisblad [z]" accesskey="z"><span>Tuisblad</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Gebruikersportaal" title="Meer oor die projek, wat jy kan doen, nuttige skakels"><span>Gebruikersportaal</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Geselshoekie" title="Agtergrondinligting oor aktuele sake"><span>Geselshoekie</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesiaal:Onlangse_wysigings" title="&#039;n Lys van onlangse wysigings [r]" accesskey="r"><span>Onlangse wysigings</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesiaal:Lukraak" title="Laai &#039;n lukrake bladsye [x]" accesskey="x"><span>Lukrake bladsy</span></a></li><li id="n-help" class="mw-list-item"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="Vind meer uit oor iets"><span>Hulp</span></a></li><li id="n-Sandput" class="mw-list-item"><a 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cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesiaal:Soek"> </div> <button class="cdx-button cdx-search-input__end-button">Soek</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Persoonlike gereedskap"> <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="Voorkoms"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page&#039;s font size, width, and color" > <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="Voorkoms" > <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">Voorkoms</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&amp;wmf_medium=sidebar&amp;wmf_campaign=af.wikipedia.org&amp;uselang=af" class=""><span>Skenkings</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=Spesiaal:SkepRekening&amp;returnto=Vlak" title="U word aangemoedig om &#039;n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie." class=""><span>Skep gebruiker</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=Spesiaal:Teken_in&amp;returnto=Vlak" title="U word aangemoedig om aan te meld. Dit is egter nie verpligtend nie. [o]" accesskey="o" class=""><span>Meld aan</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 opsies" > <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="Persoonlike gereedskap" > <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">Persoonlike gereedskap</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <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&amp;wmf_medium=sidebar&amp;wmf_campaign=af.wikipedia.org&amp;uselang=af"><span>Skenkings</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:SkepRekening&amp;returnto=Vlak" title="U word aangemoedig om &#039;n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Skep gebruiker</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:Teken_in&amp;returnto=Vlak" title="U word aangemoedig om aan te meld. Dit is egter nie verpligtend nie. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Meld aan</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"> Bladsye vir uitgemelde redakteurs <a href="/wiki/Hulp:Inleiding" aria-label="Leer meer oor redigering"><span>leer meer</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/Spesiaal:Mybydrae" title="A list of edits made from this IP address [y]" accesskey="y"><span>Bydraes</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesiaal:Mybespreking" title="Bespreking oor bydraes van hierdie IP-adres [n]" accesskey="n"><span>Bespreking</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"><!-- CentralNotice --></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="Werf"> <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">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">versteek</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">Inleiding</div> </a> </li> <li id="toc-Voorstellinge" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voorstellinge"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Voorstellinge</span> </div> </a> <button aria-controls="toc-Voorstellinge-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>Wissel Voorstellinge subafdeling</span> </button> <ul id="toc-Voorstellinge-sublist" class="vector-toc-list"> <li id="toc-Normaalvektor_en_punt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Normaalvektor_en_punt"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Normaalvektor en punt</span> </div> </a> <ul id="toc-Normaalvektor_en_punt-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Drie_punte" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Drie_punte"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Drie punte</span> </div> </a> <ul id="toc-Drie_punte-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vlakvergelyking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vlakvergelyking"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Vlakvergelyking</span> </div> </a> <ul id="toc-Vlakvergelyking-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sien_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sien_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Sien ook</span> </div> </a> <ul id="toc-Sien_ook-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" title="Inhoudsopgawe" > <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="Wissel die inhoudsopgawe" > <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">Wissel die inhoudsopgawe</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">Vlak</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="Gaan na &#039;n artikel in &#039;n ander taal. Beskikbaar in 88 tale" > <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-88" 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">88 tale</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Ebene_(Mathematik)" title="Ebene (Mathematik) – Switserse Duits" lang="gsw" hreflang="gsw" data-title="Ebene (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="Switserse Duits" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%AA%D9%88_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="مستو (رياضيات) – Arabies" lang="ar" hreflang="ar" data-title="مستو (رياضيات)" data-language-autonym="العربية" data-language-local-name="Arabies" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Planu_(xeometr%C3%ADa)" title="Planu (xeometría) – Asturies" lang="ast" hreflang="ast" data-title="Planu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="Asturies" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/M%C3%BCst%C9%99vi" title="Müstəvi – Azerbeidjans" lang="az" hreflang="az" data-title="Müstəvi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidjans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AF%D2%AB%D1%8B%D0%BB%D1%8B%D2%A1" title="Яҫылыҡ – Baskir" lang="ba" hreflang="ba" data-title="Яҫылыҡ" data-language-autonym="Башҡортса" data-language-local-name="Baskir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Плоскасць – Belarussies" lang="be" hreflang="be" data-title="Плоскасць" data-language-autonym="Беларуская" data-language-local-name="Belarussies" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D0%BE%D1%9E%D0%BD%D1%96%D1%86%D0%B0" title="Роўніца – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Роўніца" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B2%D0%BD%D0%B8%D0%BD%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Равнина (математика) – Bulgaars" lang="bg" hreflang="bg" data-title="Равнина (математика)" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%A4%E0%A6%B2" title="সমতল – Bengaals" lang="bn" hreflang="bn" data-title="সমতল" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Ravan" title="Ravan – Bosnies" lang="bs" hreflang="bs" data-title="Ravan" data-language-autonym="Bosanski" data-language-local-name="Bosnies" 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/Pla" title="Pla – Katalaans" lang="ca" hreflang="ca" data-title="Pla" data-language-autonym="Català" data-language-local-name="Katalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%AD%E1%8F%AB%E1%8E%BE%E1%8F%97%E1%8F%A2_%E1%8F%97%E1%8F%8E%E1%8F%8D%E1%8F%97_%E1%8E%A4%E1%8E%AC%E1%8F%A9%E1%8E%B5" title="ᎭᏫᎾᏗᏢ ᏗᏎᏍᏗ ᎤᎬᏩᎵ – Cherokees" lang="chr" hreflang="chr" data-title="ᎭᏫᎾᏗᏢ ᏗᏎᏍᏗ ᎤᎬᏩᎵ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="Cherokees" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%D9%88%D9%88%D8%AA%DB%95%D8%AE%D8%AA" title="ڕووتەخت – Sorani" lang="ckb" hreflang="ckb" data-title="ڕووتەخت" data-language-autonym="کوردی" data-language-local-name="Sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rovina" title="Rovina – Tsjeggies" lang="cs" hreflang="cs" data-title="Rovina" data-language-autonym="Čeština" data-language-local-name="Tsjeggies" 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%9B%D0%B0%D0%BF%D1%82%D0%B0%D0%BA" title="Лаптак – Chuvash" lang="cv" hreflang="cv" data-title="Лаптак" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Pl%C3%A2n_geometraidd" title="Plân geometraidd – Wallies" lang="cy" hreflang="cy" data-title="Plân geometraidd" data-language-autonym="Cymraeg" data-language-local-name="Wallies" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Plan_(matematik)" title="Plan (matematik) – Deens" lang="da" hreflang="da" data-title="Plan (matematik)" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Ebene_(Mathematik)" title="Ebene (Mathematik) – Duits" lang="de" hreflang="de" data-title="Ebene (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CE%BF" title="Επίπεδο – Grieks" lang="el" hreflang="el" data-title="Επίπεδο" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Euclidean_plane" title="Euclidean plane – Engels" lang="en" hreflang="en" data-title="Euclidean plane" 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/Ebeno_(matematiko)" title="Ebeno (matematiko) – Esperanto" lang="eo" hreflang="eo" data-title="Ebeno (matematiko)" 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/Plano_(geometr%C3%ADa)" title="Plano (geometría) – Spaans" lang="es" hreflang="es" data-title="Plano (geometría)" 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/Tasand" title="Tasand – Estnies" lang="et" hreflang="et" data-title="Tasand" data-language-autonym="Eesti" data-language-local-name="Estnies" 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/Plano" title="Plano – Baskies" lang="eu" hreflang="eu" data-title="Plano" data-language-autonym="Euskara" data-language-local-name="Baskies" 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/%D8%B5%D9%81%D8%AD%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="صفحه (هندسه) – Persies" lang="fa" hreflang="fa" data-title="صفحه (هندسه)" data-language-autonym="فارسی" data-language-local-name="Persies" 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/Taso" title="Taso – Fins" lang="fi" hreflang="fi" data-title="Taso" 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/Plan_(math%C3%A9matiques)" title="Plan (mathématiques) – Frans" lang="fr" hreflang="fr" data-title="Plan (mathématiques)" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Pl%C3%A1na_(matamaitic)" title="Plána (matamaitic) – Iers" lang="ga" hreflang="ga" data-title="Plána (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="Iers" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2" title="平面 – Gan-Sjinees" lang="gan" hreflang="gan" data-title="平面" data-language-autonym="贛語" data-language-local-name="Gan-Sjinees" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Plan_(mat%C3%A9matik)" title="Plan (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Plan (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Plano_(xeometr%C3%ADa)" title="Plano (xeometría) – Galisies" lang="gl" hreflang="gl" data-title="Plano (xeometría)" data-language-autonym="Galego" data-language-local-name="Galisies" 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%9E%D7%99%D7%A9%D7%95%D7%A8_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="מישור (גאומטריה) – Hebreeus" lang="he" hreflang="he" data-title="מישור (גאומטריה)" data-language-autonym="עברית" data-language-local-name="Hebreeus" 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%AE%E0%A4%A4%E0%A4%B2_(%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF)" title="समतल (ज्यामिति) – Hindi" lang="hi" hreflang="hi" data-title="समतल (ज्यामिति)" 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/Ravnina" title="Ravnina – Kroaties" lang="hr" hreflang="hr" data-title="Ravnina" data-language-autonym="Hrvatski" data-language-local-name="Kroaties" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/S%C3%ADk_(geometria)" title="Sík (geometria) – Hongaars" lang="hu" hreflang="hu" data-title="Sík (geometria)" 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%80%D5%A1%D6%80%D5%A9%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Հարթություն – Armeens" lang="hy" hreflang="hy" data-title="Հարթություն" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Plano" title="Plano – Interlingua" lang="ia" hreflang="ia" data-title="Plano" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bidang_(geometri)" title="Bidang (geometri) – Indonesies" lang="id" hreflang="id" data-title="Bidang (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesies" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Plano_(matematiko)" title="Plano (matematiko) – Ido" lang="io" hreflang="io" data-title="Plano (matematiko)" 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/Sl%C3%A9tta_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Slétta (rúmfræði) – Yslands" lang="is" hreflang="is" data-title="Slétta (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="Yslands" 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/Piano_(geometria)" title="Piano (geometria) – Italiaans" lang="it" hreflang="it" data-title="Piano (geometria)" 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/%E5%B9%B3%E9%9D%A2" title="平面 – Japannees" lang="ja" hreflang="ja" data-title="平面" data-language-autonym="日本語" data-language-local-name="Japannees" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Plien_(matimatix)" title="Plien (matimatix) – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Plien (matimatix)" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%91%E1%83%A0%E1%83%A2%E1%83%A7%E1%83%94" title="სიბრტყე – Georgies" lang="ka" hreflang="ka" data-title="სიბრტყე" data-language-autonym="ქართული" data-language-local-name="Georgies" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Agni_(tanzeggit)" title="Agni (tanzeggit) – Kabyle" lang="kab" hreflang="kab" data-title="Agni (tanzeggit)" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B0%D0%B7%D1%8B%D2%9B%D1%82%D1%8B%D2%9B_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Жазықтық (геометрия) – Kazaks" lang="kk" hreflang="kk" data-title="Жазықтық (геометрия)" data-language-autonym="Қазақша" data-language-local-name="Kazaks" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%94%E1%9F%92%E1%9E%9B%E1%9E%84%E1%9F%8B" title="ប្លង់ – Khmer" lang="km" hreflang="km" data-title="ប្លង់" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8F%89%EB%A9%B4" title="평면 – Koreaans" lang="ko" hreflang="ko" data-title="평면" 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%A2%D0%B5%D0%B3%D0%B8%D0%B7%D0%B4%D0%B8%D0%BA" title="Тегиздик – Kirgisies" lang="ky" hreflang="ky" data-title="Тегиздик" data-language-autonym="Кыргызча" data-language-local-name="Kirgisies" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Planum_(geometria)" title="Planum (geometria) – Latyn" lang="la" hreflang="la" data-title="Planum (geometria)" data-language-autonym="Latina" data-language-local-name="Latyn" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Plok%C5%A1tuma" title="Plokštuma – Litaus" lang="lt" hreflang="lt" data-title="Plokštuma" data-language-autonym="Lietuvių" data-language-local-name="Litaus" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Plakne" title="Plakne – Letties" lang="lv" hreflang="lv" data-title="Plakne" data-language-autonym="Latviešu" data-language-local-name="Letties" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Lemaka_(je%C3%B4metria)" title="Lemaka (jeômetria) – Malgassies" lang="mg" hreflang="mg" data-title="Lemaka (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="Malgassies" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Рамнина (математика) – Masedonies" lang="mk" hreflang="mk" data-title="Рамнина (математика)" data-language-autonym="Македонски" data-language-local-name="Masedonies" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Satah" title="Satah – Maleis" lang="ms" hreflang="ms" data-title="Satah" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Flach_(Mathematik)" title="Flach (Mathematik) – Nederduits" lang="nds" hreflang="nds" data-title="Flach (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="Nederduits" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vlak_(meetkunde)" title="Vlak (meetkunde) – Nederlands" lang="nl" hreflang="nl" data-title="Vlak (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="Nederlands" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Plan_i_matematikk" title="Plan i matematikk – Nuwe Noors" lang="nn" hreflang="nn" data-title="Plan i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Nuwe Noors" 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/Plan_(matematikk)" title="Plan (matematikk) – Boeknoors" lang="nb" hreflang="nb" data-title="Plan (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Boeknoors" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/P%C5%82aszczyzna" title="Płaszczyzna – Pools" lang="pl" hreflang="pl" data-title="Płaszczyzna" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Plano_(geometria)" title="Plano (geometria) – Portugees" lang="pt" hreflang="pt" data-title="Plano (geometria)" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/P%27allta" title="P&#039;allta – Quechua" lang="qu" hreflang="qu" data-title="P&#039;allta" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Plan_(geometrie)" title="Plan (geometrie) – Roemeens" lang="ro" hreflang="ro" data-title="Plan (geometrie)" 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%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Плоскость – Russies" lang="ru" hreflang="ru" data-title="Плоскость" data-language-autonym="Русский" data-language-local-name="Russies" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A5%D0%B0%D0%BF%D1%82%D0%B0%D0%BB" title="Хаптал – Jakoeties" lang="sah" hreflang="sah" data-title="Хаптал" data-language-autonym="Саха тыла" data-language-local-name="Jakoeties" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ravan" title="Ravan – Serwo-Kroaties" lang="sh" hreflang="sh" data-title="Ravan" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serwo-Kroaties" 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/Plane_(mathematics)" title="Plane (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Plane (mathematics)" 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/Rovina_(geometria)" title="Rovina (geometria) – Slowaaks" lang="sk" hreflang="sk" data-title="Rovina (geometria)" 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/Ravnina" title="Ravnina – Sloweens" lang="sl" hreflang="sl" data-title="Ravnina" data-language-autonym="Slovenščina" data-language-local-name="Sloweens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mutsendo" title="Mutsendo – Shona" lang="sn" hreflang="sn" data-title="Mutsendo" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrafshi_Euklidian" title="Rrafshi Euklidian – Albanees" lang="sq" hreflang="sq" data-title="Rrafshi Euklidian" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B2%D0%B0%D0%BD" title="Раван – Serwies" lang="sr" hreflang="sr" data-title="Раван" data-language-autonym="Српски / srpski" data-language-local-name="Serwies" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Plan_(geometri)" title="Plan (geometri) – Sweeds" lang="sv" hreflang="sv" data-title="Plan (geometri)" data-language-autonym="Svenska" data-language-local-name="Sweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%B3%E0%AE%AE%E0%AF%8D_(%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D)" title="தளம் (வடிவவியல்) – Tamil" lang="ta" hreflang="ta" data-title="தளம் (வடிவவியல்)" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%99%E0%B8%B2%E0%B8%9A" title="ระนาบ – Thai" lang="th" hreflang="th" data-title="ระนาบ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Plano_(heometriya)" title="Plano (heometriya) – Tagalog" lang="tl" hreflang="tl" data-title="Plano (heometriya)" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/D%C3%BCzlem" title="Düzlem – Turks" lang="tr" hreflang="tr" data-title="Düzlem" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AF%D1%81%D1%81%D1%8B%D0%BB%D1%8B%D0%BA_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Яссылык (математика) – Tataars" lang="tt" hreflang="tt" data-title="Яссылык (математика)" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B8%D0%BD%D0%B0" title="Площина – Oekraïens" lang="uk" hreflang="uk" data-title="Площина" 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/%D9%85%D8%B3%D8%AA%D9%88%DB%8C_(%DB%81%D9%86%D8%AF%D8%B3%DB%81)" title="مستوی (ہندسہ) – Oerdoe" lang="ur" hreflang="ur" data-title="مستوی (ہندسہ)" data-language-autonym="اردو" data-language-local-name="Oerdoe" 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/Tekislik" title="Tekislik – Oesbekies" lang="uz" hreflang="uz" data-title="Tekislik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oesbekies" 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/M%E1%BA%B7t_ph%E1%BA%B3ng_(to%C3%A1n_h%E1%BB%8Dc)" title="Mặt phẳng (toán học) – Viëtnamees" lang="vi" hreflang="vi" data-title="Mặt phẳng (toán học)" data-language-autonym="Tiếng Việt" data-language-local-name="Viëtnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Plano_(heyometriya)" title="Plano (heyometriya) – Waray" lang="war" hreflang="war" data-title="Plano (heyometriya)" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2" title="平面 – Wu-Sjinees" lang="wuu" hreflang="wuu" data-title="平面" data-language-autonym="吴语" data-language-local-name="Wu-Sjinees" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%9C%D7%90%D7%9A" title="פלאך – Jiddisj" lang="yi" hreflang="yi" data-title="פלאך" data-language-autonym="ייִדיש" data-language-local-name="Jiddisj" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学) – Chinees" lang="zh" hreflang="zh" data-title="平面 (数学)" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/P%C3%AE%E2%81%BF-b%C4%ABn" title="Pîⁿ-bīn – Min Nan-Sjinees" lang="nan" hreflang="nan" data-title="Pîⁿ-bīn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Min Nan-Sjinees" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何) – Kantonees" lang="yue" hreflang="yue" data-title="面 (幾何)" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</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/Q17285#sitelinks-wikipedia" title="Wysig skakels tussen tale" class="wbc-editpage">Wysig skakels</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="Naamruimtes"> <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/Vlak" title="Bekyk die inhoudbladsy [c]" accesskey="c"><span>Bladsy</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Bespreking:Vlak" rel="discussion" title="Bespreking oor die inhoudbladsy [t]" accesskey="t"><span>Bespreking</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" aria-haspopup="true" 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href="/wiki/Vlak"><span>Lees</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vlak&amp;veaction=edit" title="Redigeer hierdie bladsy [v]" accesskey="v"><span>Wysig</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vlak&amp;action=edit" title="Wysig die bladsy se bonkode [e]" accesskey="e"><span>Wysig bron</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vlak&amp;action=history" title="Ouer weergawes van hierdie bladsy [h]" accesskey="h"><span>Wys geskiedenis</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" 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href="/w/index.php?title=Vlak&amp;action=edit" title="Wysig die bladsy se bonkode [e]" accesskey="e"><span>Wysig bron</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vlak&amp;action=history"><span>Wys geskiedenis</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/Spesiaal:Skakels_hierheen/Vlak" title="&#039;n Lys bladsye wat hierheen skakel [j]" accesskey="j"><span>Skakels hierheen</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesiaal:OnlangseVeranderingsMetSkakels/Vlak" rel="nofollow" title="Onlangse wysigings aan bladsye wat vanaf hierdie bladsy geskakel is [k]" accesskey="k"><span>Verwante veranderings</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Vlak&amp;oldid=1644432" title="&#039;n Permanente skakel na hierdie weergawe van die bladsy"><span>Permanente skakel</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Vlak&amp;action=info" title="More information about this page"><span>Bladinligting</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:CiteThisPage&amp;page=Vlak&amp;id=1644432&amp;wpFormIdentifier=titleform" title="Inligting oor hoe u hierdie bladsy kan verwys"><span>Haal dié blad aan</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:UrlShortener&amp;url=https%3A%2F%2Faf.wikipedia.org%2Fwiki%2FVlak"><span>Kry verkorte URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:QrCode&amp;url=https%3A%2F%2Faf.wikipedia.org%2Fwiki%2FVlak"><span>Laai QR-kode af</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"> Druk/uitvoer </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=Spesiaal:Boek&amp;bookcmd=book_creator&amp;referer=Vlak"><span>Skep boek</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:DownloadAsPdf&amp;page=Vlak&amp;action=show-download-screen"><span>Laai af as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Vlak&amp;printable=yes" title="Drukbare weergawe van hierdie bladsy [p]" accesskey="p"><span>Drukbare weergawe</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"> Ander projekte </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:Euclidean_planes" 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/Q17285" title="Skakel na gekonnekteerde databank item [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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Voorkoms"> <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">Voorkoms</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">versteek</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">in Wikipedia, die vrye ensiklopedie</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="af" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:PlaneIntersection.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/PlaneIntersection.png/220px-PlaneIntersection.png" decoding="async" width="220" height="239" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/PlaneIntersection.png/330px-PlaneIntersection.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/PlaneIntersection.png/440px-PlaneIntersection.png 2x" data-file-width="497" data-file-height="539" /></a><figcaption>Twee vlakke wat mekaar sny.</figcaption></figure> <p>'n <b>Meetkundige vlak</b> is 'n plat, oneindige vlak, met 'n oneindige oppervlakte. Dit deel 'n driedimensionele ruimte in twee. Hierdie twee deelruimtes word <b>halfruimtes</b> genoem. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Voorstellinge">Voorstellinge</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vlak&amp;veaction=edit&amp;section=1" title="Wysig afdeling: Voorstellinge" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vlak&amp;action=edit&amp;section=1" title="Edit section&#39;s source code: Voorstellinge"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jy kan 'n vlak op verskeie maniere voorstel. Ons beskryf hier die mees gebruikte metode: </p> <div class="mw-heading mw-heading3"><h3 id="Normaalvektor_en_punt">Normaalvektor en punt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vlak&amp;veaction=edit&amp;section=2" title="Wysig afdeling: Normaalvektor en punt" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vlak&amp;action=edit&amp;section=2" title="Edit section&#39;s source code: Normaalvektor en punt"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>'n <a href="/wiki/Vektor" class="mw-redirect" title="Vektor">Vektor</a> loodreg op die vlak N(x,y,z), die <a href="/w/index.php?title=Normaalvektor&amp;action=edit&amp;redlink=1" class="new" title="Normaalvektor (bladsy bestaan nie)">normaalvektor</a>, bepaal die oriëntasie van die vlak. Die presiese ligging van die vlak is hiermee nog nie vasgestel nie, maar dit kan gedoen word deur 'n punt P(x0,y0,z0) in die vlak te benoem. </p> <div class="mw-heading mw-heading3"><h3 id="Drie_punte">Drie punte</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vlak&amp;veaction=edit&amp;section=3" title="Wysig afdeling: Drie punte" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vlak&amp;action=edit&amp;section=3" title="Edit section&#39;s source code: Drie punte"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As jy drie punte het wat nie almal op een lyn in 'n vlak geleë is nie, dan is die vlak daarmee eenduidig vasgestel. </p> <div class="mw-heading mw-heading3"><h3 id="Vlakvergelyking">Vlakvergelyking</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vlak&amp;veaction=edit&amp;section=4" title="Wysig afdeling: Vlakvergelyking" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vlak&amp;action=edit&amp;section=4" title="Edit section&#39;s source code: Vlakvergelyking"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elke vlak voldoen aan die vergelyking: </p> <pre>a*x + b*y + c*z + d = 0 </pre> <p>Hierby is (a,b,c) die normaalvektor van hierdie vlak. As daar soos in die eerste beskrywing 'n punt P(x0,y0,z0) in die vlak bekend is, kan jy die waarde d hieruit bepaal met die volgende formule: </p> <pre>d = -a*x0 – b*y0 – c*z0 </pre> <p>As daar soos in die tweede vergelyking drie punte bekend is, dan kan jy die normaalvektor bepaal deur van die driehoek wat die punte vorm twee sye te neem. Hierdie twee sye is twee rigtingsvektore in die vlak. Deur die <a href="/w/index.php?title=Uitwendige_produk&amp;action=edit&amp;redlink=1" class="new" title="Uitwendige produk (bladsy bestaan nie)">uitwendige produk</a> tussen hierdie vektore te neem verkry jy 'n normaalvektor, waarna jy die prosedure hierbo kan gebruik. </p> <div class="mw-heading mw-heading2"><h2 id="Sien_ook">Sien ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vlak&amp;veaction=edit&amp;section=5" title="Wysig afdeling: Sien ook" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vlak&amp;action=edit&amp;section=5" title="Edit section&#39;s source code: Sien ook"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-base, #fff);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></td> <td class="mbox-text plainlist">Sien <i><b><a href="https://af.wiktionary.org/wiki/vlak" class="extiw" title="wikt:vlak">vlak</a></b></i> in Wiktionary, die vrye woordeboek.</td></tr></tbody></table> <ul><li><a href="/w/index.php?title=Tweedimensioneel&amp;action=edit&amp;redlink=1" class="new" title="Tweedimensioneel (bladsy bestaan nie)">Tweedimensioneel</a></li> <li><a href="/wiki/Driedimensioneel" title="Driedimensioneel">Driedimensioneel</a></li> <li><a href="/wiki/Oppervlakte" title="Oppervlakte">Oppervlakte</a></li></ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐6458bccbb8‐2c2tp Cached time: 20250209184804 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.035 seconds Real time usage: 0.051 seconds Preprocessor visited node count: 101/1000000 Post‐expand include size: 1800/2097152 bytes Template argument size: 87/2097152 bytes Highest expansion depth: 9/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 0/5000000 bytes Lua time usage: 0.005/10.000 seconds Lua memory usage: 586437/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 26.532 1 Sjabloon:Wikt 100.00% 26.532 1 -total 92.91% 24.650 1 Sjabloon:Susterprojek 85.67% 22.729 1 Sjabloon:Sykas --> <!-- Saved in parser cache with key afwiki:pcache:6283:|#|:idhash:canonical and timestamp 20250209184804 and revision id 1644432. 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aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Wissel die inhoudsopgawe" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-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">Wissel die inhoudsopgawe</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Vlak</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>88 tale</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Nuwe onderwerp</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-7f5d45d576-ncbzw","wgBackendResponseTime":137,"wgPageParseReport":{"limitreport":{"cputime":"0.035","walltime":"0.051","ppvisitednodes":{"value":101,"limit":1000000},"postexpandincludesize":{"value":1800,"limit":2097152},"templateargumentsize":{"value":87,"limit":2097152},"expansiondepth":{"value":9,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":0,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 26.532 1 Sjabloon:Wikt","100.00% 26.532 1 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