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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">Início</div> </a> </li> <li id="toc-Nomenclatura" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nomenclatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Nomenclatura</span> </div> </a> <ul id="toc-Nomenclatura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Escolha_da_origem" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Escolha_da_origem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Escolha da origem</span> </div> </a> <ul id="toc-Escolha_da_origem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sistema_cartesiano" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sistema_cartesiano"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Sistema cartesiano</span> </div> </a> <ul id="toc-Sistema_cartesiano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Posição</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="Ir para um artigo noutra língua. Disponível em 49 línguas" > <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-49" 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">49 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AA%D8%AC%D9%87_%D9%85%D9%88%D8%B6%D8%B9" title="متجه موضع — árabe" lang="ar" hreflang="ar" data-title="متجه موضع" data-language-autonym="العربية" data-language-local-name="árabe" 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%A0%D0%B0%D0%B4%D1%8B%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%B0%D1%80" title="Радыус-вектар — bielorrusso" lang="be" hreflang="be" data-title="Радыус-вектар" data-language-autonym="Беларуская" data-language-local-name="bielorrusso" 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%B0%D0%B4%D1%8B%D1%8E%D1%81-%D0%B2%D1%8D%D0%BA%D1%82%D0%B0%D1%80" title="Радыюс-вэктар — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Радыюс-вэктар" 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%B4%D0%B8%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Радиус-вектор — búlgaro" lang="bg" hreflang="bg" data-title="Радиус-вектор" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8B%E0%A4%9C%E0%A5%80%E0%A4%B6%E0%A4%A8_(%E0%A4%B5%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%9F%E0%A4%B0)" title="पोजीशन (वेक्टर) — Bhojpuri" lang="bh" hreflang="bh" data-title="पोजीशन (वेक्टर)" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A7_%E0%A6%AD%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%9F%E0%A6%B0" title="ব্যাসার্ধ ভেক্টর — bengalês" lang="bn" hreflang="bn" data-title="ব্যাসার্ধ ভেক্টর" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Posici%C3%B3" title="Posició — catalão" lang="ca" hreflang="ca" data-title="Posició" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B4%D9%88%DB%8E%D9%86" title="شوێن — curdo central" lang="ckb" hreflang="ckb" data-title="شوێن" data-language-autonym="کوردی" data-language-local-name="curdo central" 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/Polohov%C3%BD_vektor" title="Polohový vektor — checo" lang="cs" hreflang="cs" data-title="Polohový vektor" data-language-autonym="Čeština" data-language-local-name="checo" 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%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Радиус-вектор — chuvash" lang="cv" hreflang="cv" data-title="Радиус-вектор" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Stedvektor" title="Stedvektor — dinamarquês" lang="da" hreflang="da" data-title="Stedvektor" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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/Ortsvektor" title="Ortsvektor — alemão" lang="de" hreflang="de" data-title="Ortsvektor" data-language-autonym="Deutsch" data-language-local-name="alemão" 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%98%CE%AD%CF%83%CE%B7" title="Θέση — grego" lang="el" hreflang="el" data-title="Θέση" data-language-autonym="Ελληνικά" data-language-local-name="grego" 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/Position_(geometry)" title="Position (geometry) — inglês" lang="en" hreflang="en" data-title="Position (geometry)" data-language-autonym="English" data-language-local-name="inglês" 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/Situa_vektoro" title="Situa vektoro — esperanto" lang="eo" hreflang="eo" data-title="Situa vektoro" 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/Posici%C3%B3n" title="Posición — espanhol" lang="es" hreflang="es" data-title="Posición" data-language-autonym="Español" data-language-local-name="espanhol" 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/Kohavektor" title="Kohavektor — estónio" lang="et" hreflang="et" data-title="Kohavektor" data-language-autonym="Eesti" data-language-local-name="estónio" 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/Egongune" title="Egongune — basco" lang="eu" hreflang="eu" data-title="Egongune" data-language-autonym="Euskara" data-language-local-name="basco" 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%A8%D8%B1%D8%AF%D8%A7%D8%B1_%D9%85%DA%A9%D8%A7%D9%86" title="بردار مکان — persa" lang="fa" hreflang="fa" data-title="بردار مکان" data-language-autonym="فارسی" data-language-local-name="persa" 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/Paikkavektori" title="Paikkavektori — finlandês" lang="fi" hreflang="fi" data-title="Paikkavektori" data-language-autonym="Suomi" data-language-local-name="finlandês" 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/Vecteur_position" title="Vecteur position — francês" lang="fr" hreflang="fr" data-title="Vecteur position" data-language-autonym="Français" data-language-local-name="francês" 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/Posici%C3%B3n_(xeometr%C3%ADa)" title="Posición (xeometría) — galego" lang="gl" hreflang="gl" data-title="Posición (xeometría)" data-language-autonym="Galego" data-language-local-name="galego" 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%A7%D7%95%D7%9D_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="מיקום (גאומטריה) — hebraico" lang="he" hreflang="he" data-title="מיקום (גאומטריה)" data-language-autonym="עברית" data-language-local-name="hebraico" 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%A5%8D%E0%A4%A5%E0%A4%BF%E0%A4%A4%E0%A4%BF_%E0%A4%B8%E0%A4%A6%E0%A4%BF%E0%A4%B6" title="स्थिति सदिश — hindi" lang="hi" hreflang="hi" data-title="स्थिति सदिश" 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/Radijvektor" title="Radijvektor — croata" lang="hr" hreflang="hr" data-title="Radijvektor" data-language-autonym="Hrvatski" data-language-local-name="croata" 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/Helyvektor" title="Helyvektor — húngaro" lang="hu" hreflang="hu" data-title="Helyvektor" data-language-autonym="Magyar" data-language-local-name="húngaro" 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%87%D5%A1%D5%BC%D5%A1%D5%BE%D5%AB%D5%B2-%D5%BE%D5%A5%D5%AF%D5%BF%D5%B8%D6%80" title="Շառավիղ-վեկտոր — arménio" lang="hy" hreflang="hy" data-title="Շառավիղ-վեկտոր" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Posisi_(vektor)" title="Posisi (vektor) — indonésio" lang="id" hreflang="id" data-title="Posisi (vektor)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Posizione" title="Posizione — italiano" lang="it" hreflang="it" data-title="Posizione" data-language-autonym="Italiano" data-language-local-name="italiano" 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/%E4%BD%8D%E7%BD%AE" title="位置 — japonês" lang="ja" hreflang="ja" data-title="位置" data-language-autonym="日本語" data-language-local-name="japonês" 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%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Радиус-вектор — cazaque" lang="kk" hreflang="kk" data-title="Радиус-вектор" data-language-autonym="Қазақша" data-language-local-name="cazaque" 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/%EC%9C%84%EC%B9%98%EB%B2%A1%ED%84%B0" title="위치벡터 — coreano" lang="ko" hreflang="ko" data-title="위치벡터" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Полупречнички вектор — macedónio" lang="mk" hreflang="mk" data-title="Полупречнички вектор" data-language-autonym="Македонски" data-language-local-name="macedónio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Plaatsvector" title="Plaatsvector — neerlandês" lang="nl" hreflang="nl" data-title="Plaatsvector" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Posisjonsvektor" title="Posisjonsvektor — norueguês bokmål" lang="nb" hreflang="nb" data-title="Posisjonsvektor" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês 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%AA%E0%A9%81%E0%A8%9C%E0%A9%80%E0%A8%B8%E0%A8%BC%E0%A8%A8" title="ਪੁਜੀਸ਼ਨ — panjabi" lang="pa" hreflang="pa" data-title="ਪੁਜੀਸ਼ਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" 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/Wektor_wodz%C4%85cy" title="Wektor wodzący — polaco" lang="pl" hreflang="pl" data-title="Wektor wodzący" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Радиус-вектор — russo" lang="ru" hreflang="ru" data-title="Радиус-вектор" data-language-autonym="Русский" data-language-local-name="russo" 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/Polo%C5%BEaj_(geometrija)" title="Položaj (geometrija) — servo-croata" lang="sh" hreflang="sh" data-title="Položaj (geometrija)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="servo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Krajevni_vektor" title="Krajevni vektor — esloveno" lang="sl" hreflang="sl" data-title="Krajevni vektor" data-language-autonym="Slovenščina" data-language-local-name="esloveno" 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/Pozicioni_(gjeometri)" title="Pozicioni (gjeometri) — albanês" lang="sq" hreflang="sq" data-title="Pozicioni (gjeometri)" data-language-autonym="Shqip" data-language-local-name="albanês" 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%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D0%BF%D0%BE%D0%BB%D0%BE%D0%B6%D0%B0%D1%98%D0%B0" title="Вектор положаја — sérvio" lang="sr" hreflang="sr" data-title="Вектор положаја" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" 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/Ortsvektor" title="Ortsvektor — sueco" lang="sv" hreflang="sv" data-title="Ortsvektor" data-language-autonym="Svenska" data-language-local-name="sueco" 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%A8%E0%AE%BF%E0%AE%B2%E0%AF%88%E0%AE%A4%E0%AF%8D_%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%AF%E0%AE%A9%E0%AF%8D" title="நிலைத் திசையன் — tâmil" lang="ta" hreflang="ta" data-title="நிலைத் திசையன்" data-language-autonym="தமிழ்" data-language-local-name="tâmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%96%D1%83%D1%81-%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Радіус-вектор — ucraniano" lang="uk" hreflang="uk" data-title="Радіус-вектор" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Holat_(geometriya)" title="Holat (geometriya) — usbeque" lang="uz" hreflang="uz" data-title="Holat (geometriya)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" 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/V%E1%BB%8B_tr%C3%AD_(vector)" title="Vị trí (vector) — vietnamita" lang="vi" hreflang="vi" data-title="Vị trí (vector)" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" 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/%E4%BD%8D%E7%BD%AE%E5%90%91%E9%87%8F" title="位置向量 — chinês" lang="zh" hreflang="zh" data-title="位置向量" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BD%8D%E7%BD%AE" title="位置 — cantonês" lang="yue" hreflang="yue" data-title="位置" data-language-autonym="粵語" data-language-local-name="cantonês" 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/Q192388#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</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="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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0;border-collapse:collapse;border:1px solid #c0c090;background-color:#f8eaba;box-sizing:border-box}.mw-parser-output .tmbox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .tmbox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .tmbox-delete{border:2px solid #b32424}.mw-parser-output .tmbox-content{border:1px solid #c0c090}.mw-parser-output .tmbox-style{border:2px solid #fc3}.mw-parser-output .tmbox-move{border:2px solid #9932cc}.mw-parser-output .tmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .tmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .tmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .tmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .tmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .tmbox{margin:4px 10%}.mw-parser-output .tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Mais_notas plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Question_book-new.svg" class="mw-file-description"><img alt="Esta página cita fontes, mas não cobrem todo o conteúdo" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Esta página <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cita fontes</a>, mas que <b><a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">não cobrem</a> todo o conteúdo</b>.<span class="hide-when-compact"> Ajude a <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserir referências</a> (<small><i>Encontre fontes:</i> <span class="plainlinks"><a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/">ABW</a>  •  <a rel="nofollow" class="external text" href="https://www.periodicos.capes.gov.br">CAPES</a>  •  <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&as_epq=Posi%C3%A7%C3%A3o">Google</a> (<a rel="nofollow" class="external text" href="https://www.google.com/search?hl=pt&tbm=nws&q=Posi%C3%A7%C3%A3o&oq=Posi%C3%A7%C3%A3o">N</a> • <a rel="nofollow" class="external text" href="http://books.google.com/books?&as_brr=0&as_epq=Posi%C3%A7%C3%A3o">L</a> • <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?hl=pt&q=Posi%C3%A7%C3%A3o">A</a>)</span></small>).</span> <small class="date-container"><i>(<span class="date">Maio de 2018</span>)</i></small></div></td></tr></tbody></table> <div class="hatnote"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/20px-Disambig_grey.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/30px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/40px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> <b>Nota:</b> Para outros significados, veja <a href="/wiki/Posi%C3%A7%C3%A3o_(desambigua%C3%A7%C3%A3o)" class="mw-disambig" title="Posição (desambiguação)">Posição (desambiguação)</a>.</div> <p>Em <a href="/wiki/F%C3%ADsica" title="Física">física</a>, a <b>posição</b> de um corpo é a especificação de seu lugar no <a href="/wiki/Espa%C3%A7o" class="mw-disambig" title="Espaço">espaço</a>. A identificação da posição é feita a partir de um <a href="/wiki/Vetor_(matem%C3%A1tica)" title="Vetor (matemática)">vetor</a>, denominado vetor posição, que pode ser escrito em função de um <a href="/wiki/Sistema_de_coordenadas" title="Sistema de coordenadas">sistema de coordenadas</a> de um certo <a href="/wiki/Referencial" title="Referencial">referencial</a>. A <a href="/wiki/Unidade_de_medida" title="Unidade de medida">unidade de medida</a> da posição no <a href="/wiki/Sistema_Internacional_de_Unidades" title="Sistema Internacional de Unidades">Sistema Internacional de Unidades</a> é o <a href="/wiki/Metro" title="Metro">metro</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Nomenclatura">Nomenclatura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&veaction=edit&section=1" title="Editar secção: Nomenclatura" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&action=edit&section=1" title="Editar código-fonte da secção: Nomenclatura"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Para localizar a posição de um objeto no espaço são necessárias três medidas. Existe certa liberdade em como uma pessoa escolhe estas três medidas, chamadas de <a href="/wiki/Coordenadas" class="mw-disambig" title="Coordenadas">coordenadas</a> do objeto. Isto da origem a diversos <b>sistemas de coordenadas</b> possíveis e todos são igualmente bons. No entanto, em alguns casos, a escolha do sistema de coordenada pode simplificar bastante a solução de um problema. </p><p>Pelo fato de termos que utilizar três medidas para localizar o objeto dizemos então que o espaço tem <b>três dimensões</b>. Se o objeto estivesse sobre uma mesa, e estivéssemos apenas interessado na posição do mesmo sobre ela, poderíamos descartar uma das medidas e portando estaríamos lidando com um espaço com <b>duas dimensões.</b> </p> <div class="mw-heading mw-heading2"><h2 id="Escolha_da_origem">Escolha da origem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&veaction=edit&section=2" title="Editar secção: Escolha da origem" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&action=edit&section=2" title="Editar código-fonte da secção: Escolha da origem"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Para localizar os objetos de seu interesse, primeiro é necessário escolher uma origem. A origem é o ponto de onde se sairá medindo as distâncias até os objetos. Qualquer ponto serve para a origem, mas algumas vezes existem pontos especiais que simplificam a tarefa. Por exemplo em uma sala, os cantos da sala podem ser ótimos pontos para se escolher a origem. </p> <div class="mw-heading mw-heading2"><h2 id="Sistema_cartesiano">Sistema cartesiano</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&veaction=edit&section=3" title="Editar secção: Sistema cartesiano" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posi%C3%A7%C3%A3o&action=edit&section=3" title="Editar código-fonte da secção: Sistema cartesiano"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File"><a href="/wiki/Ficheiro:Plano_coord.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Plano_coord.svg/319px-Plano_coord.svg.png" decoding="async" width="319" height="283" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Plano_coord.svg/479px-Plano_coord.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Plano_coord.svg/638px-Plano_coord.svg.png 2x" data-file-width="319" data-file-height="283" /></a><figcaption></figcaption></figure> <p>Neste sistema utilizamos três distâncias de um ponto até a origem. Considerando que você esta em uma sala, estas três distâncias podem ser: </p> <dl><dd>A altura do objeto do solo (coordenada z)</dd> <dd>A distancia do objeto até uma das paredes que passa pelo canto escolhido como origem (coordenada x) e</dd> <dd>A distância até a parede adjacente a origem (coordenada y).</dd></dl> <p>A ordem em que estas distâncias é escolhida não é relevante, desde que se mantenha a consistência nas medidas. Para simplificar a contabilidade destas medidas utiliza-se uma lista com os valores. Suponha que os valores encontrados sejam, z = 1 metro, y = 3 metros, e x = 2 metros. Podemos escrever a posição do objeto desta forma: </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 {\frac {}{}}(x,y,z)=(2,3,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow /> <mrow /> </mfrac> </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> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {}{}}(x,y,z)=(2,3,1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7540e83834c5b5568d2f28179437b9c0e7cf75f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.75ex; height:3.843ex;" alt="{\displaystyle {\frac {}{}}(x,y,z)=(2,3,1)}"></span></dd></dl> <p>O motivo de escrever as medidas desta forma é para permitir utilizarmos o conceito de <a href="/wiki/Vetor" class="mw-disambig" title="Vetor">vetores</a>. Com este formalismo podemos não só localizar os objetos, como também calcular a distância entre eles em um dado instante. Além disto, após aprendermos como trabalhar com estes conceitos em duas ou três dimensões podemos facilmente generalizar estas ideias para qualquer dimensão. Isto é, com o mesmo raciocínio usado aqui e uma notação 'esperta', podemos calcular distâncias, e muito mais, em qualquer dimensão. </p> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite class="citation book">União Internacional de Química Pura e Aplicada (2018). <a rel="nofollow" class="external text" href="http://www.sbq.org.br/livroverde/anexos/LivroVerde_IUPAC_SBQ-SPQ_2018.pdf"><i>Grandezas, Unidades e Símbolos em Físico-Química</i></a> <span style="font-size:85%;">(PDF)</span> 3 ed. São Paulo: Sociedade Brasileira de Química e Sociedade Portuguesa de Química. p. 13</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APosi%C3%A7%C3%A3o&rft.au=Uni%C3%A3o+Internacional+de+Qu%C3mica+Pura+e+Aplicada&rft.btitle=Grandezas%2C+Unidades+e+S%C3mbolos+em+F%C3sico-Qu%C3mica&rft.date=2018&rft.edition=3&rft.genre=book&rft.pages=13&rft.place=S%C3%A3o+Paulo&rft.pub=Sociedade+Brasileira+de+Qu%C3mica+e+Sociedade+Portuguesa+de+Qu%C3mica&rft_id=http%3A%2F%2Fwww.sbq.org.br%2Flivroverde%2Fanexos%2FLivroVerde_IUPAC_SBQ-SPQ_2018.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="noprint" style="clear: right; border: solid #aaa 1px; margin: 0 0 1em 1em; font-size: 90%; background: var(--background-color-neutral-subtle, #f9f9f9); color: inherit; width: 250px; padding: 5px; spacing: 2px; text-align: center; float: right;"> <div style="float: left; vertical-align:middle;"><figure class="mw-halign-none" typeof="mw:File"><span title="Wikcionário"><img alt="Wikcionário" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/40px-Wiktionary-logo.svg.png" decoding="async" width="40" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/60px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/80px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></span><figcaption>Wikcionário</figcaption></figure></div> <div style="margin-left: 30px; line-height:normal; vertical-align:middle;">O <a href="/wiki/Wikcion%C3%A1rio" title="Wikcionário">Wikcionário</a> tem o verbete <i><b><a href="https://pt.wiktionary.org/wiki/Posi%C3%A7%C3%A3o" class="extiw" title="wikt:Posição">Posição</a></b></i>.</div></div> <div role="navigation" class="navbox" aria-labelledby="Controle_de_autoridade" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Controle_de_autoridade" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Ajuda:Controle_de_autoridade" title="Ajuda:Controle de autoridade">Controle de autoridade</a></th><td class="navbox-list navbox-odd plainlinks" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Wikidata:Main_Page" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span>: <span class="uid"><a href="https://www.wikidata.org/wiki/Q192388" class="extiw" title="wikidata:Q192388">Q192388</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Grande_Enciclop%C3%A9dia_Sovi%C3%A9tica" title="Grande Enciclopédia Soviética">BRE</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://old.bigenc.ru/text/3490028">3490028</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">EBID</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/position-vector">ID</a></span></span></span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtida de "<a dir="ltr" href="https://pt.wikipedia.org/w/index.php?title=Posição&oldid=64667790">https://pt.wikipedia.org/w/index.php?title=Posição&oldid=64667790</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categorias</a>: <ul><li><a href="/wiki/Categoria:Mec%C3%A2nica" title="Categoria:Mecânica">Mecânica</a></li><li><a href="/wiki/Categoria:Sistemas_de_coordenadas" title="Categoria:Sistemas de coordenadas">Sistemas de coordenadas</a></li><li><a href="/wiki/Categoria:Posi%C3%A7%C3%A3o" title="Categoria:Posição">Posição</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorias ocultas: <ul><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_desde_maio_de_2018" title="Categoria:!Artigos que carecem de notas de rodapé desde maio de 2018">!Artigos que carecem de notas de rodapé desde maio de 2018</a></li><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_sem_indica%C3%A7%C3%A3o_de_tema" title="Categoria:!Artigos que carecem de notas de rodapé sem indicação de tema">!Artigos que carecem de notas de rodapé sem indicação de tema</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Esta página foi editada pela última vez às 15h58min de 2 de novembro de 2022.</li> <li id="footer-info-copyright">Este texto é disponibilizado nos termos da licença <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pt">Atribuição-CompartilhaIgual 4.0 Internacional (CC BY-SA 4.0) da Creative Commons</a>; 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