{"id":402,"date":"2023-06-19T11:39:22","date_gmt":"2023-06-19T11:39:22","guid":{"rendered":"https:\/\/physigeek.com\/tr\/vektor-pozisyonu\/"},"modified":"2023-06-19T11:39:22","modified_gmt":"2023-06-19T11:39:22","slug":"vektor-pozisyonu","status":"publish","type":"post","link":"https:\/\/physigeek.com\/tr\/vektor-pozisyonu\/","title":{"rendered":"Vekt\u00f6r pozisyonu"},"content":{"rendered":"<p>Bu makale fizikte konum vekt\u00f6r\u00fcn\u00fcn ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece konum vekt\u00f6r\u00fcn\u00fcn \u00f6zelliklerinin neler oldu\u011funu, bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve ayr\u0131ca ad\u0131m ad\u0131m somut bir \u00f6rnek ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-vector-de-posicion\"><\/span> Konum vekt\u00f6r\u00fc nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir <strong>konum vekt\u00f6r\u00fc<\/strong> veya basit\u00e7e <strong>bir konum vekt\u00f6r\u00fc<\/strong> , bir noktan\u0131n bir referans sistemine g\u00f6re konumunu tan\u0131mlayan bir vekt\u00f6rd\u00fcr. Yani konum vekt\u00f6r\u00fc, bir koordinat sistemindeki bir noktan\u0131n konumunu belirtmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Matematiksel olarak bir noktan\u0131n konum vekt\u00f6r\u00fc, koordinatlar\u0131n orijininden o noktaya giden vekt\u00f6r olarak tan\u0131mlan\u0131r. Bu nedenle bir noktan\u0131n konum vekt\u00f6r\u00fc, o noktan\u0131n koordinatlar\u0131ndan orijin koordinatlar\u0131n\u0131n \u00e7\u0131kar\u0131lmas\u0131yla hesaplan\u0131r.<\/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> Genel olarak konum vekt\u00f6r\u00fc birim vekt\u00f6rlerle ifade edilir.<\/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> Ve<\/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&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;438&#8243; width=&#8221;1546&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn koordinatlar\u0131 birim vekt\u00f6rlerle ifade edilir\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> Ve<\/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}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;41&#8243; width=&#8221;616&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> <span style=\"color:#101010;font-weight: normal;\">Konum vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc, i\u015faretin ba\u015flang\u0131\u00e7 noktas\u0131n\u0131 dikkate al\u0131nan noktaya ba\u011flayan \u00e7izgidir.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Konum vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc orijinden \u00e7al\u0131\u015fma noktas\u0131na do\u011frudur.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc, nokta ile koordinatlar\u0131n orijini aras\u0131ndaki mesafedir. Konum vekt\u00f6r\u00fcn\u00fcn normu, koordinatlar\u0131n\u0131n karelerinin toplam\u0131n\u0131n karek\u00f6k\u00fcne e\u015fittir.<\/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> D\u00fczlemde \u00e7al\u0131\u015f\u0131yorsak konum vekt\u00f6r\u00fcn\u00fcn yaln\u0131zca iki koordinata (x,y) sahip olaca\u011f\u0131n\u0131 unutmay\u0131n. \u00d6te yandan uzayda \u00e7al\u0131\u015f\u0131yorsak konum vekt\u00f6r\u00fcn\u00fcn \u00fc\u00e7 koordinat\u0131 (x,y,z) olacakt\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-del-vector-de-posicion\"><\/span> Konum vekt\u00f6r\u00fc al\u0131\u015ft\u0131rmas\u0131 \u00e7\u00f6z\u00fcld\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Konsepti iyi anlamak i\u00e7in a\u015fa\u011f\u0131da konum vekt\u00f6r\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131na ili\u015fkin \u00e7\u00f6z\u00fcml\u00fc bir al\u0131\u015ft\u0131rma bulunmaktad\u0131r.<\/p>\n<ul>\n<li> Bir cismin konum-zaman vekt\u00f6r\u00fc a\u015fa\u011f\u0131daki ifadeyle tan\u0131mlan\u0131r. Cismin t=3 s an\u0131ndaki konum vekt\u00f6r\u00fcn\u00fc ve mod\u00fcl\u00fcn\u00fc hesaplay\u0131n\u0131z.<\/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> t=3 s zaman\u0131ndaki konum vekt\u00f6r\u00fcn\u00fc bulmak i\u00e7in t parametresini de\u011feriyle de\u011fi\u015ftirmeli ve hesaplamalar\u0131 yapmal\u0131s\u0131n\u0131z:<\/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> Daha sonra koordinatlar\u0131n kareleri toplam\u0131n\u0131n karek\u00f6k\u00fcn\u00fc hesaplayarak konum vekt\u00f6r\u00fcn\u00fcn mod\u00fcl\u00fcn\u00fc \u00e7\u0131kar\u0131r\u0131z: <\/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> Konum ve yer de\u011fi\u015ftirme vekt\u00f6r\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir noktan\u0131n <strong>ofseti,<\/strong> biti\u015f noktas\u0131 ile ba\u015flang\u0131\u00e7 noktas\u0131 aras\u0131ndaki mesafe olarak tan\u0131mlan\u0131r. Dolay\u0131s\u0131yla yer de\u011fi\u015ftirme vekt\u00f6r\u00fc, son konum vekt\u00f6r\u00fcnden ba\u015flang\u0131\u00e7 konum vekt\u00f6r\u00fcn\u00fcn \u00e7\u0131kar\u0131lmas\u0131yla elde edilen vekt\u00f6rd\u00fcr.<\/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> Dolay\u0131s\u0131yla <strong>konum vekt\u00f6r\u00fc ile yer de\u011fi\u015ftirme aras\u0131ndaki fark<\/strong> , konum vekt\u00f6r\u00fcn\u00fcn bir cismin belirli bir andaki konumunu g\u00f6stermesi, \u00f6te yandan yer de\u011fi\u015ftirme vekt\u00f6r\u00fcn\u00fcn ise hareketli bir cismin iki farkl\u0131 konumu aras\u0131ndaki mesafeyi g\u00f6stermesidir. <\/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> Ayn\u0131 \u015fekilde rotan\u0131n hareketi de farkl\u0131la\u015ft\u0131r\u0131lmal\u0131d\u0131r. Yol, gidilen yolun toplam uzunlu\u011funu belirtirken, yer de\u011fi\u015ftirme son konumdan son konuma olan mesafeyi belirtir. Bu nedenle yol, uzakl\u0131ktan daha b\u00fcy\u00fck olabilir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale fizikte konum vekt\u00f6r\u00fcn\u00fcn ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece konum vekt\u00f6r\u00fcn\u00fcn \u00f6zelliklerinin neler oldu\u011funu, bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve ayr\u0131ca ad\u0131m ad\u0131m somut bir \u00f6rnek ke\u015ffedeceksiniz. Konum vekt\u00f6r\u00fc nedir? Bir konum vekt\u00f6r\u00fc veya basit\u00e7e bir konum vekt\u00f6r\u00fc , bir noktan\u0131n bir referans sistemine g\u00f6re konumunu tan\u0131mlayan bir vekt\u00f6rd\u00fcr. Yani konum vekt\u00f6r\u00fc, bir koordinat &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/tr\/vektor-pozisyonu\/\"> <span class=\"screen-reader-text\">Vekt\u00f6r pozisyonu<\/span> Devam\u0131 &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-sinematik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Vekt\u00f6r\u00fc konumland\u0131r\u0131n<\/title>\n<meta name=\"description\" content=\"Burada konum vekt\u00f6r\u00fcn\u00fcn ne oldu\u011funu, \u00f6zelliklerini, konum vekt\u00f6r\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/physigeek.com\/tr\/vektor-pozisyonu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Vekt\u00f6r\u00fc konumland\u0131r\u0131n\" \/>\n<meta property=\"og:description\" content=\"Burada konum vekt\u00f6r\u00fcn\u00fcn ne oldu\u011funu, \u00f6zelliklerini, konum vekt\u00f6r\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physigeek.com\/tr\/vektor-pozisyonu\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-19T11:39:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-94a2838c46b47b0de3fbc3ab9548365c_l3.png\" \/>\n<meta name=\"author\" content=\"Jonathan Reynolds\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Jonathan Reynolds\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" 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