{"id":402,"date":"2023-06-19T11:39:22","date_gmt":"2023-06-19T11:39:22","guid":{"rendered":"https:\/\/physigeek.com\/nl\/positievector\/"},"modified":"2023-06-19T11:39:22","modified_gmt":"2023-06-19T11:39:22","slug":"positievector","status":"publish","type":"post","link":"https:\/\/physigeek.com\/nl\/positievector\/","title":{"rendered":"Positievector"},"content":{"rendered":"<p>In dit artikel wordt uitgelegd wat de positievector in de natuurkunde is. Zo ontdekt u stap voor stap wat de eigenschappen van de positievector zijn, hoe u de positievector van een punt berekent en ook een concreet voorbeeld. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-vector-de-posicion\"><\/span> Wat is een positievector?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Een <strong>positievector<\/strong> , of eenvoudigweg <strong>een positievector<\/strong> , is een vector die de positie van een punt ten opzichte van een referentiesysteem beschrijft. Dat wil zeggen dat de positievector wordt gebruikt om de positie van een punt in een co\u00f6rdinatensysteem aan te geven.<\/p>\n<p> Wiskundig gezien wordt de positievector van een punt gedefinieerd als de vector die van de oorsprong van de co\u00f6rdinaten naar dat punt gaat. Daarom wordt de positievector van een punt berekend door de co\u00f6rdinaten van dat punt af te trekken minus de oorsprongsco\u00f6rdinaten.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-94a2838c46b47b0de3fbc3ab9548365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r_{p}}=PO\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Over het algemeen wordt de positievector uitgedrukt door de eenheidsvectoren<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0b35266aff72392f18054a3ee0726b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e64160920c9450edf06e8f621fe04ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{j}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-493ea824d13cdf2c289249ee201f0079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{k}[\/latex ] , qui correspondent respectivement aux coordonn\u00e9es des axes X, Y et Z. Par exemple, si les coordonn\u00e9es cart\u00e9siennes d'un point sont (3,4,5), le vecteur position de ce point est r=3i+4j+5k. \n\n<figure class=&quot;wp-block-image aligncenter size-full is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position.png&quot; alt=&quot;vecteur de position&quot; class=&quot;wp-image-7644&quot; width=&quot;374&quot; height=&quot;308&quot; srcset=&quot;https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-300x247.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position.png 697w&quot; sizes=&quot;(max-width: 300px) 100vw, 300px&quot;><\/figure>\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;Caracteristicas-del-vector-de-posicion&quot;><\/span> Caract\u00e9ristiques du vecteur de position<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> Maintenant que nous connaissons la d\u00e9finition du vecteur position, voyons quelles sont ses caract\u00e9ristiques.<\/p>\n<ul style=&quot;color:#4fd12f; font-weight: bold;&quot;>\n<li style=&quot;margin-bottom:20px&quot;> <span style=&quot;color:#101010;font-weight: normal;&quot;>Le vecteur position d&#8217;un point est d\u00e9fini comme la diff\u00e9rence entre les coordonn\u00e9es de ce point et l&#8217;origine des coordonn\u00e9es. Par cons\u00e9quent, la formule pour calculer le vecteur position d&#8217;un point est la suivante :<\/span><\/li>\n<p> [latex]\\vv{r}=PO&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;438&#8243; width=&#8220;1546&#8243; style=&#8220;vertical-align: -5px;&#8220;><\/p>\n<\/p>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">De co\u00f6rdinaten van de positievector van een punt worden uitgedrukt door de eenheidsvectoren\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0b35266aff72392f18054a3ee0726b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e64160920c9450edf06e8f621fe04ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{j}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> En<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9a41deb220b0257eea947e8a946f9a2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{k}[ \/latex], qui repr\u00e9sentent respectivement les directions des axes OX, OY et OZ.<\/span><\/li>\n<p> [latex]\\vv{r}=x\\vv{i}+y\\vv{j}+z\\vv{k}&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;41&#8243; width=&#8220;616&#8243; style=&#8220;vertical-align: -5px;&#8220;><\/p>\n<p> <span style=\"color:#101010;font-weight: normal;\">De richting van de positievector is de lijn die de oorsprong van het merkteken verbindt met het beschouwde punt.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">De richting van de positievector loopt van de oorsprong naar het studiepunt.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">De grootte van de positievector van een punt is de afstand tussen het punt en de oorsprong van de co\u00f6rdinaten. De norm van de positievector is gelijk aan de vierkantswortel van de som van de kwadraten van zijn co\u00f6rdinaten.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-4e00e2651473f9b281caa2edb84af61b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{r}|=\\sqrt{x^2+y^2+z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Merk op dat de positievector slechts twee co\u00f6rdinaten (x,y) zal hebben als we in het vlak werken. Aan de andere kant, als we in de ruimte werken, heeft de positievector drie co\u00f6rdinaten (x,y,z). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-del-vector-de-posicion\"><\/span> Positievectoroefening opgelost<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Om het concept goed te begrijpen, vindt u hieronder een opgeloste oefening over hoe de positievector wordt berekend.<\/p>\n<ul>\n<li> De positie versus tijdvector van een lichaam wordt gedefinieerd door de onderstaande uitdrukking. Bereken de positievector van het lichaam op tijdstip t=3 s en zijn module.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-03e3237c194135f352830e0617712fdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}(t)=4t\\vv{i}+2t^2\\vv{j}+5 \\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"166\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Om de positievector op tijdstip t=3 s te vinden, moet je de parameter t vervangen door zijn waarde en de berekeningen uitvoeren:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-dec24ff071b35d8e731e7a0a66d6c0e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\vv{r}(3)&amp;=4\\cdot 3\\vv{i}+2\\cdot 3^2\\vv{j}+5 \\vv{k}\\\\[2ex ]\\vv{r}(3)&amp;=12\\vv{i}+18\\vv{j}+5\\vv{k}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Vervolgens voeren we de module van de positievector uit door de vierkantswortel te berekenen van de som van de kwadraten van de co\u00f6rdinaten: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c09dc9fc6db4d03b23adfc1b44c8168_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}|\\vv{r}(3)|&amp;=\\sqrt{12^2+18^2+5^2}\\\\[2ex]|\\vv{r}(3)| &amp;=\\sqrt{493}\\end{align\u00e9}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"191\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Vector-de-posicion-y-desplazamiento\"><\/span> Positie- en verplaatsingsvector<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>offset<\/strong> van een punt wordt gedefinieerd als de afstand tussen het eindpunt en het startpunt. Daarom is de verplaatsingsvector de vector die wordt verkregen door de eindpositievector minus de initi\u00eble positievector af te trekken.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-c75a87e8719ce716eb129379b32a9966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\vv{r}=\\vv{r_2}-\\vv{r_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Het <strong>verschil tussen de positievector en de verplaatsing<\/strong> is dus dat de positievector de positie van een lichaam op een bepaald moment aangeeft, terwijl de verplaatsingsvector daarentegen de afstand tussen twee verschillende posities van een bewegend lichaam aangeeft. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-et-de-deplacement.png\" alt=\"\" class=\"wp-image-7663\" width=\"324\" height=\"263\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-et-de-deplacement-300x243.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-et-de-deplacement.png 650w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Op dezelfde manier moet de beweging van de route gedifferentieerd zijn. Pad verwijst naar de totale lengte van het afgelegde pad, terwijl verplaatsing verwijst naar de afstand van de eindpositie naar de eindpositie. Het pad kan daarom groter zijn dan de offset.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel wordt uitgelegd wat de positievector in de natuurkunde is. Zo ontdekt u stap voor stap wat de eigenschappen van de positievector zijn, hoe u de positievector van een punt berekent en ook een concreet voorbeeld. Wat is een positievector? Een positievector , of eenvoudigweg een positievector , is een vector die de &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/nl\/positievector\/\"> <span class=\"screen-reader-text\">Positievector<\/span> Weiterlesen &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-402","post","type-post","status-publish","format-standard","hentry","category-filmisch"],"yoast_head":"<!-- This site is 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