{"id":402,"date":"2023-06-19T11:39:22","date_gmt":"2023-06-19T11:39:22","guid":{"rendered":"https:\/\/physigeek.com\/ja\/%e4%bd%8d%e7%bd%ae%e3%83%98%e3%82%99%e3%82%af%e3%83%88%e3%83%ab\/"},"modified":"2023-06-19T11:39:22","modified_gmt":"2023-06-19T11:39:22","slug":"%e4%bd%8d%e7%bd%ae%e3%83%98%e3%82%99%e3%82%af%e3%83%88%e3%83%ab","status":"publish","type":"post","link":"https:\/\/physigeek.com\/ja\/%e4%bd%8d%e7%bd%ae%e3%83%98%e3%82%99%e3%82%af%e3%83%88%e3%83%ab\/","title":{"rendered":"\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7269\u7406\u5b66\u306b\u304a\u3051\u308b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u7279\u6027\u3001\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u65b9\u6cd5\u3001\u304a\u3088\u3073\u5177\u4f53\u7684\u306a\u4f8b\u3092\u6bb5\u968e\u7684\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-vector-de-posicion\"><\/span>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/strong>\u3001\u307e\u305f\u306f\u5358\u306b<strong>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb \u306f<\/strong>\u3001\u57fa\u6e96\u7cfb\u306b\u5bfe\u3059\u308b\u70b9\u306e\u4f4d\u7f6e\u3092\u8a18\u8ff0\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u5ea7\u6a19\u7cfb\u5185\u306e\u70b9\u306e\u4f4d\u7f6e\u3092\u793a\u3059\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u6570\u5b66\u7684\u306b\u306f\u3001\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u5ea7\u6a19\u306e\u539f\u70b9\u304b\u3089\u305d\u306e\u70b9\u306b\u5411\u304b\u3046\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u305d\u306e\u70b9\u306e\u5ea7\u6a19\u304b\u3089\u539f\u70b9\u5ea7\u6a19\u3092\u6e1b\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\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\u306b\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u8868\u73fe\u3055\u308c\u307e\u3059\u3002<\/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> \u3001<\/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>\u305d\u3057\u3066<\/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\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19\u306f\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u8868\u73fe\u3055\u308c\u307e\u3059\u3002\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> \u3001<\/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>\u305d\u3057\u3066<\/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\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u30de\u30fc\u30af\u306e\u539f\u70b9\u3068\u5bfe\u8c61\u306e\u70b9\u3092\u7d50\u3076\u7dda\u3067\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u539f\u70b9\u304b\u3089\u8abf\u67fb\u70b9\u3078\u306e\u65b9\u5411\u3067\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306f\u3001\u305d\u306e\u70b9\u3068\u5ea7\u6a19\u306e\u539f\u70b9\u306e\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u30ce\u30eb\u30e0\u306f\u3001\u305d\u306e\u5ea7\u6a19\u306e\u4e8c\u4e57\u548c\u306e\u5e73\u65b9\u6839\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\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>\u5e73\u9762\u5185\u3067\u4f5c\u696d\u3059\u308b\u5834\u5408\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u306f 2 \u3064\u306e\u5ea7\u6a19 (x,y) \u3057\u304b\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e00\u65b9\u3001\u7a7a\u9593\u3067\u4f5c\u696d\u3059\u308b\u5834\u5408\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u306f 3 \u3064\u306e\u5ea7\u6a19 (x\u3001y\u3001z) \u304c\u542b\u307e\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-del-vector-de-posicion\"><\/span>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6f14\u7fd2\u304c\u89e3\u6c7a\u3055\u308c\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6982\u5ff5\u3092\u3088\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u306b\u3064\u3044\u3066\u306e\u6f14\u7fd2\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7269\u4f53\u306e\u4f4d\u7f6e\u3068\u6642\u9593\u306e\u30d9\u30af\u30c8\u30eb\u306f\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u6642\u523b t=3 \u79d2\u306b\u304a\u3051\u308b\u7269\u4f53\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u305d\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u8a08\u7b97\u3057\u307e\u3059\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>\u6642\u523b t=3 s \u3067\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc t \u3092\u305d\u306e\u5024\u306b\u7f6e\u304d\u63db\u3048\u3066\u8a08\u7b97\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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-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>\u6b21\u306b\u3001\u5ea7\u6a19\u306e\u4e8c\u4e57\u548c\u306e\u5e73\u65b9\u6839\u3092\u8a08\u7b97\u3057\u3066\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u51fa\u529b\u3057\u307e\u3059\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-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\u3068\u5909\u4f4d\u30d9\u30af\u30c8\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u70b9\u306e<strong>\u30aa\u30d5\u30bb\u30c3\u30c8\u306f\u3001<\/strong>\u7d42\u70b9\u3068\u59cb\u70b9\u306e\u9593\u306e\u8ddd\u96e2\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5909\u4f4d\u30d9\u30af\u30c8\u30eb\u306f\u3001\u6700\u7d42\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304b\u3089\u521d\u671f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5f15\u3044\u305f\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\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>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u5909\u4f4d\u306e\u9055\u3044<\/strong>\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u7279\u5b9a\u306e\u6642\u523b\u306b\u304a\u3051\u308b\u7269\u4f53\u306e\u4f4d\u7f6e\u3092\u793a\u3059\u306e\u306b\u5bfe\u3057\u3001\u5909\u4f4d\u30d9\u30af\u30c8\u30eb\u306f\u79fb\u52d5\u4f53\u306e 2 \u3064\u306e\u7570\u306a\u308b\u4f4d\u7f6e\u9593\u306e\u8ddd\u96e2\u3092\u793a\u3059\u3053\u3068\u3067\u3059\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, 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