{"id":402,"date":"2023-06-19T11:39:22","date_gmt":"2023-06-19T11:39:22","guid":{"rendered":"https:\/\/physigeek.com\/cn\/%e4%bd%8d%e7%bd%ae%e5%90%91%e9%87%8f\/"},"modified":"2023-06-19T11:39:22","modified_gmt":"2023-06-19T11:39:22","slug":"%e4%bd%8d%e7%bd%ae%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/physigeek.com\/cn\/%e4%bd%8d%e7%bd%ae%e5%90%91%e9%87%8f\/","title":{"rendered":"\u4f4d\u7f6e\u5411\u91cf"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7269\u7406\u5b66\u4e2d\u7684\u4f4d\u7f6e\u5411\u91cf\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u9010\u6b65\u4e86\u89e3\u4f4d\u7f6e\u5411\u91cf\u7684\u5c5e\u6027\u662f\u4ec0\u4e48\u3001\u5982\u4f55\u8ba1\u7b97\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u4ee5\u53ca\u5177\u4f53\u793a\u4f8b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-vector-de-posicion\"><\/span>\u4ec0\u4e48\u662f\u4f4d\u7f6e\u5411\u91cf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f4d\u7f6e\u5411\u91cf<\/strong>\uff0c\u6216\u7b80\u79f0<strong>\u4e3a\u4f4d\u7f6e\u5411\u91cf<\/strong>\uff0c\u662f\u63cf\u8ff0\u70b9\u76f8\u5bf9\u4e8e\u53c2\u8003\u7cfb\u7684\u4f4d\u7f6e\u7684\u5411\u91cf\u3002\u5373\u4f4d\u7f6e\u5411\u91cf\u7528\u4e8e\u8868\u793a\u5750\u6807\u7cfb\u4e2d\u70b9\u7684\u4f4d\u7f6e\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u8bb2\uff0c\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u5b9a\u4e49\u4e3a\u4ece\u5750\u6807\u539f\u70b9\u5230\u8be5\u70b9\u7684\u5411\u91cf\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u5c06\u8be5\u70b9\u7684\u5750\u6807\u51cf\u53bb\u539f\u70b9\u5750\u6807\u6765\u8ba1\u7b97\u8be5\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u3002<\/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>\u4e00\u822c\u6765\u8bf4\uff0c\u4f4d\u7f6e\u5411\u91cf\u7528\u5355\u4f4d\u5411\u91cf\u8868\u793a<\/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>\u548c<\/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;\">\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u7684\u5750\u6807\u7528\u5355\u4f4d\u5411\u91cf\u8868\u793a\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>\u548c<\/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;\">\u4f4d\u7f6e\u77e2\u91cf\u7684\u65b9\u5411\u662f\u5c06\u6807\u8bb0\u539f\u70b9\u4e0e\u6240\u8003\u8651\u7684\u70b9\u8fde\u63a5\u8d77\u6765\u7684\u7ebf\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u4f4d\u7f6e\u77e2\u91cf\u7684\u65b9\u5411\u662f\u4ece\u539f\u70b9\u5230\u7814\u7a76\u70b9\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u7684\u5927\u5c0f\u662f\u8be5\u70b9\u4e0e\u5750\u6807\u539f\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u4f4d\u7f6e\u5411\u91cf\u7684\u8303\u6570\u7b49\u4e8e\u5176\u5750\u6807\u5e73\u65b9\u548c\u7684\u5e73\u65b9\u6839\u3002<\/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>\u8bf7\u6ce8\u610f\uff0c\u5982\u679c\u6211\u4eec\u5728\u5e73\u9762\u4e0a\u5de5\u4f5c\uff0c\u4f4d\u7f6e\u5411\u91cf\u5c06\u53ea\u6709\u4e24\u4e2a\u5750\u6807 (x,y)\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6211\u4eec\u5728\u7a7a\u95f4\u4e2d\u5de5\u4f5c\uff0c\u4f4d\u7f6e\u5411\u91cf\u5c06\u5177\u6709\u4e09\u4e2a\u5750\u6807\uff08x\uff0cy\uff0cz\uff09\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-del-vector-de-posicion\"><\/span>\u4f4d\u7f6e\u5411\u91cf\u7ec3\u4e60\u5df2\u89e3\u51b3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u5173\u4e8e\u5982\u4f55\u8ba1\u7b97\u4f4d\u7f6e\u5411\u91cf\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\u3002<\/p>\n<ul>\n<li>\u7269\u4f53\u7684\u4f4d\u7f6e\u4e0e\u65f6\u95f4\u5411\u91cf\u7531\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u5b9a\u4e49\u3002\u8ba1\u7b97 t=3 s \u65f6\u523b\u7269\u4f53\u7684\u4f4d\u7f6e\u5411\u91cf\u53ca\u5176\u6a21\u3002<\/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>\u8981\u627e\u5230\u65f6\u95f4 t=3 s \u65f6\u7684\u4f4d\u7f6e\u5411\u91cf\uff0c\u60a8\u5fc5\u987b\u5c06\u53c2\u6570 t \u66ff\u6362\u4e3a\u5176\u503c\u5e76\u8fdb\u884c\u8ba1\u7b97\uff1a<\/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>\u7136\u540e\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u5750\u6807\u5e73\u65b9\u548c\u7684\u5e73\u65b9\u6839\u6765\u8f93\u51fa\u4f4d\u7f6e\u5411\u91cf\u7684\u6a21\uff1a <\/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>\u4f4d\u7f6e\u548c\u4f4d\u79fb\u77e2\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u70b9\u7684<strong>\u504f\u79fb<\/strong>\u5b9a\u4e49\u4e3a\u7ec8\u70b9\u4e0e\u8d77\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u56e0\u6b64\uff0c\u4f4d\u79fb\u77e2\u91cf\u5c31\u662f\u6700\u7ec8\u4f4d\u7f6e\u77e2\u91cf\u51cf\u53bb\u521d\u59cb\u4f4d\u7f6e\u77e2\u91cf\u5f97\u5230\u7684\u77e2\u91cf\u3002<\/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>\u56e0\u6b64\uff0c<strong>\u4f4d\u7f6e\u77e2\u91cf\u548c\u4f4d\u79fb\u4e4b\u95f4\u7684\u533a\u522b<\/strong>\u5728\u4e8e\uff0c\u4f4d\u7f6e\u77e2\u91cf\u8868\u793a\u7269\u4f53\u5728\u7ed9\u5b9a\u65f6\u95f4\u7684\u4f4d\u7f6e\uff0c\u800c\u4f4d\u79fb\u77e2\u91cf\u8868\u793a\u8fd0\u52a8\u7269\u4f53\u7684\u4e24\u4e2a\u4e0d\u540c\u4f4d\u7f6e\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002 <\/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>\u540c\u6837\uff0c\u8def\u7ebf\u7684\u79fb\u52a8\u4e5f\u5fc5\u987b\u6709\u6240\u533a\u522b\u3002\u8def\u5f84\u662f\u6307\u8d70\u8fc7\u7684\u8def\u5f84\u7684\u603b\u957f\u5ea6\uff0c\u800c\u4f4d\u79fb\u662f\u6307\u4ece\u6700\u7ec8\u4f4d\u7f6e\u5230\u6700\u7ec8\u4f4d\u7f6e\u7684\u8ddd\u79bb\u3002\u56e0\u6b64\uff0c\u8def\u5f84\u53ef\u4ee5\u5927\u4e8e\u504f\u79fb\u91cf\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7269\u7406\u5b66\u4e2d\u7684\u4f4d\u7f6e\u5411\u91cf\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u9010\u6b65\u4e86\u89e3\u4f4d\u7f6e\u5411\u91cf\u7684\u5c5e\u6027\u662f\u4ec0\u4e48\u3001\u5982\u4f55\u8ba1\u7b97\u70b9\u7684\u4f4d\u7f6e\u5411\u91cf\u4ee5\u53ca\u5177\u4f53\u793a\u4f8b\u3002 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/cn\/%e4%bd%8d%e7%bd%ae%e5%90%91%e9%87%8f\/\"> <span class=\"screen-reader-text\">\u4f4d\u7f6e\u5411\u91cf<\/span> \u67e5\u770b\u5168\u6587 &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-3"],"yoast_head":"<!-- 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