{"id":401,"date":"2023-06-19T11:39:22","date_gmt":"2023-06-19T11:39:22","guid":{"rendered":"https:\/\/physigeek.com\/id\/vektor-posisi\/"},"modified":"2023-06-19T11:39:22","modified_gmt":"2023-06-19T11:39:22","slug":"vektor-posisi","status":"publish","type":"post","link":"https:\/\/physigeek.com\/id\/vektor-posisi\/","title":{"rendered":"Vektor posisi"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu vektor posisi dalam fisika. Dengan demikian, Anda akan mengetahui apa saja sifat-sifat vektor posisi, cara menghitung vektor posisi suatu titik, dan juga contoh nyata langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-vector-de-posicion\"><\/span> Apa yang dimaksud dengan vektor posisi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Vektor posisi<\/strong> , atau sederhananya <strong>vektor posisi<\/strong> , adalah vektor yang menggambarkan posisi suatu titik relatif terhadap sistem referensi. Artinya, vektor posisi digunakan untuk menunjukkan posisi suatu titik dalam suatu sistem koordinat.<\/p>\n<p> Secara matematis, vektor posisi suatu titik didefinisikan sebagai vektor yang berpindah dari titik asal ke titik tersebut. Oleh karena itu, vektor posisi suatu titik dihitung dengan mengurangkan koordinat titik tersebut dikurangi koordinat asal.<\/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> Secara umum, vektor posisi dinyatakan dengan vektor satuan<\/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> Dan<\/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;\">Koordinat vektor posisi suatu titik dinyatakan dengan vektor satuan\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> Dan<\/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;\">Arah vektor posisi adalah garis yang menghubungkan titik asal tanda dengan titik yang ditinjau.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Arah vektor posisi adalah dari titik asal sampai titik penelitian.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Besaran vektor posisi suatu titik adalah jarak antara titik tersebut dengan titik asal koordinat. Norma vektor posisi sama dengan akar kuadrat dari jumlah kuadrat koordinatnya.<\/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> Perhatikan bahwa vektor posisi hanya akan memiliki dua koordinat (x,y) jika kita bekerja pada bidang. Sebaliknya jika kita bekerja di ruang angkasa, vektor posisi akan memiliki tiga koordinat (x,y,z). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-del-vector-de-posicion\"><\/span> Latihan vektor posisi terpecahkan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk memahami konsep ini dengan baik, di bawah ini adalah latihan tentang cara menghitung vektor posisi.<\/p>\n<ul>\n<li> Vektor posisi versus waktu suatu benda ditentukan oleh ekspresi di bawah ini. Hitung vektor posisi benda pada waktu t=3 s dan modulnya.<\/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> Untuk mencari vektor posisi pada waktu t=3 s Anda harus mengganti parameter t dengan nilainya dan melakukan perhitungan:<\/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> Kemudian kita mengeluarkan modul vektor posisi dengan menghitung akar kuadrat dari jumlah kuadrat koordinat: <\/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> Vektor posisi dan perpindahan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Offset<\/strong> suatu titik didefinisikan sebagai jarak antara titik akhir dan titik awal. Oleh karena itu, vektor perpindahan adalah vektor yang diperoleh dengan mengurangkan vektor posisi akhir dikurangi vektor posisi awal.<\/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> Oleh karena itu, <strong>perbedaan antara vektor posisi dan perpindahan<\/strong> adalah bahwa vektor posisi menunjukkan posisi suatu benda pada waktu tertentu, sebaliknya vektor perpindahan menunjukkan jarak antara dua posisi benda bergerak yang berbeda. <\/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=\"(max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Begitu pula pergerakan rutenya harus dibedakan. Lintasan mengacu pada total panjang lintasan yang ditempuh, sedangkan perpindahan mengacu pada jarak dari posisi akhir ke posisi akhir. Oleh karena itu, jalurnya bisa lebih besar daripada offsetnya.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu vektor posisi dalam fisika. Dengan demikian, Anda akan mengetahui apa saja sifat-sifat vektor posisi, cara menghitung vektor posisi suatu titik, dan juga contoh nyata langkah demi langkah. Apa yang dimaksud dengan vektor posisi? Vektor posisi , atau sederhananya vektor posisi , adalah vektor yang menggambarkan posisi suatu titik relatif terhadap &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/id\/vektor-posisi\/\"> <span class=\"screen-reader-text\">Vektor posisi<\/span> Baca selengkapnya &quot;<\/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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 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