{"id":268,"date":"2023-07-10T02:22:55","date_gmt":"2023-07-10T02:22:55","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%a8%e3%81%af%e4%bd%95%e3%81%a7%e3%81%99%e3%81%8b-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86%e5%ad%a6%e3%81%ae%e4%be%8b\/"},"modified":"2023-07-10T02:22:55","modified_gmt":"2023-07-10T02:22:55","slug":"%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%a8%e3%81%af%e4%bd%95%e3%81%a7%e3%81%99%e3%81%8b-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86%e5%ad%a6%e3%81%ae%e4%be%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%a8%e3%81%af%e4%bd%95%e3%81%a7%e3%81%99%e3%81%8b-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86%e5%ad%a6%e3%81%ae%e4%be%8b\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\uff08\u6570\u5b66\uff09\u3068\u306f\u4f55\u3067\u3059\u304b?"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u304b\u3001\u305d\u306e\u7279\u5fb4\u3001\u8a08\u7b97\u65b9\u6cd5\u3001\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u305f\u6f14\u7b97\u306e\u65b9\u6cd5\u3001\u5b58\u5728\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u30bf\u30a4\u30d7\u306a\u3069\u3001\u30d9\u30af\u30c8\u30eb\u306b\u95a2\u3059\u308b\u3059\u3079\u3066\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-vector\"><\/span>\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<p>\u6570\u5b66\u3067\u306f\u3001<strong>\u30d9\u30af\u30c8\u30eb\u306f\u3001\u3042\u308b\u70b9 (\u539f\u70b9\u3068\u547c\u3070\u308c\u308b) \u304b\u3089\u5225\u306e\u70b9 (\u7d42\u70b9\u3068\u547c\u3070\u308c\u308b) \u306b\u5411\u304b\u3046\u6709\u5411\u7dda\u5206\u3067\u3059\u3002<\/strong><\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u304c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-243865b783ec40e03ec861ac2ebcb279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u59cb\u70b9\u3068\u3057\u3066\u70b9 A \u304c\u3042\u308a\u3001\u7d42\u70b9\u3068\u3057\u3066\u70b9 B \u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quest-ce-quun-vecteur.webp\" alt=\"\u6570\u5b66\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u3067\u3059\u304b\" class=\"wp-image-3678\" width=\"176\" height=\"176\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u30d9\u30af\u30c8\u30eb\u306f\u4e3b\u306b\u6570\u5b66\u3001\u7279\u306b\u5e7e\u4f55\u5b66\u3084\u7269\u7406\u5b66\u3067\u30d9\u30af\u30c8\u30eb\u529b\u3092\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u3067\u8868\u3059\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-un-vector\"><\/span>\u30d9\u30af\u30c8\u30eb\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u6570\u5b66\u7684\u610f\u5473\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u6b21\u306b\u305d\u306e\u7279\u6027\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5404\u30d9\u30af\u30c8\u30eb\u306b\u306f\u6b21\u306e\u5e7e\u4f55\u5b66\u7684\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>\u65b9\u5411<\/strong>: \u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3092\u542b\u3080\u7dda\u3001\u307e\u305f\u306f\u305d\u308c\u306b\u5e73\u884c\u306a\u7dda\u306e\u65b9\u5411\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u305d\u306e\u30d9\u30af\u30c8\u30eb\u304c\u4e57\u3063\u3066\u3044\u308b\u76f4\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u65b9\u5411<\/strong>: \u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u77e2\u5370\u3067\u793a\u3055\u308c\u308b\u5f53\u8a72\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u3067\u3059\u3002<\/li>\n<li><strong>\u30e2\u30b8\u30e5\u30fc\u30eb<\/strong>(\u307e\u305f\u306f\u5927\u304d\u3055): \u30d9\u30af\u30c8\u30eb\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u305d\u306e\u9577\u3055\u3067\u3042\u308a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u6570\u5024\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d9\u30af\u30c8\u30eb\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u305d\u308c\u304c\u8868\u3059\u30d9\u30af\u30c8\u30eb\u91cf\u3082\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u9069\u7528\u70b9<\/strong>: \u30d9\u30af\u30c8\u30eb\u306e\u9069\u7528\u70b9\u306f\u3001\u305d\u306e\u30d9\u30af\u30c8\u30eb\u306e\u539f\u70b9\u3067\u3059\u3002 <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/caracteristiques-d-un-vecteur.webp\" alt=\"\u30d9\u30af\u30c8\u30eb\u306e\u5e7e\u4f55\u5b66\u7684\u7279\u5fb4\" class=\"wp-image-3682\" width=\"332\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u65b9\u5411\u3068\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306e\u6982\u5ff5\u306f\u6df7\u540c\u3055\u308c\u3084\u3059\u3044\u305f\u3081\u3001\u4e21\u8005\u306e\u9055\u3044\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u542b\u3080\u6b21\u306e\u4f8b\u3092\u898b\u3066\u304f\u3060\u3055\u3044\u3002\u3069\u3061\u3089\u3082\u65b9\u5411\u306f\u540c\u3058\u3067\u3059\u304c\u3001\u610f\u5473\u304c\u7570\u306a\u308a\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/sens-et-direction-d-un-vecteur.webp\" alt=\"\u30d9\u30af\u30c8\u30eb\u306e\u610f\u5473\u3068\u65b9\u5411\u306e\u610f\u5473\" class=\"wp-image-3686\" width=\"446\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u5e73\u884c\u3067\u3042\u308b\u305f\u3081\u3001\u540c\u3058\u65b9\u5411\u306b\u306a\u308a\u307e\u3059\u3002\u4ee3\u308f\u308a\u306b\u3001\u305d\u308c\u3089\u306f\u5f8c\u308d\u3092\u5411\u3044\u3066\u3044\u308b\u305f\u3081\u3001\u65b9\u5411\u304c\u9006\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"componentes-de-un-vector\"><\/span> \u30d9\u30af\u30c8\u30eb\u306e\u69cb\u6210\u8981\u7d20<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d9\u30af\u30c8\u30eb\u304c\u77e2\u5370\u306b\u3088\u3063\u3066\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u8868\u73fe\u3055\u308c\u308b\u3053\u3068\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u30d9\u30af\u30c8\u30eb\u306f\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206 (\u307e\u305f\u306f\u5ea7\u6a19) \u306b\u3088\u3063\u3066\u6570\u5024\u7684\u306b\u8868\u73fe\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u30d9\u30af\u30c8\u30eb\u304c\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteur-exemples.webp\" alt=\"\u30d9\u30af\u30c8\u30eb\u306e\u4f8b\" class=\"wp-image-3692\" width=\"316\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9\u3068\u7d42\u70b9\u306e\u5ea7\u6a19\u3001\u3064\u307e\u308a\u59cb\u70b9\u3068\u7d42\u70b9\u306e\u5ea7\u6a19\u3092\u7279\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9\u3068\u7d42\u70b9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-center\">\u30d9\u30af\u30c8\u30eb\u306e\u539f\u70b9: A(2,1)<\/p>\n<p class=\"has-text-align-center\">\u30d9\u30af\u30c8\u30eb\u306e\u7d42\u70b9: B(5,6)<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19\u307e\u305f\u306f\u6210\u5206\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u7d42\u70b9\u304b\u3089\u539f\u70b9\u3092\u5f15\u304f\u3060\u3051\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fba10729c8ded7f7c7051cfda5c12eab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{AB} &amp; = B- A \\\\[2ex] &amp; = (5,6)- (2,1) \\\\[2ex] &amp;= (5-2 \\ , \\ 6-1) \\\\[2ex] &amp;= (3,5) \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"144\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u308b\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8fbf31faea8cf602f9556fa80f618515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\bm{AB}}\\bm{=(3,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"operaciones-con-vectores\"><\/span>\u30d9\u30af\u30c8\u30eb\u6f14\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"suma-de-vectores\"><\/span>\u30d9\u30af\u30c8\u30eb\u306e\u8ffd\u52a0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u6570\u5024\u7684\u306b\u52a0\u7b97\u3059\u308b\u306b\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3092\u52a0\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e X \u5ea7\u6a19\u306f\u52a0\u7b97\u3055\u308c\u3001Y \u5ea7\u6a19\u3068\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d97d089a143f6e30d987b0ed74c56dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} + \\vv{\\text{v}} = (\\text{u}_x + \\text{v}_x \\ , \\ \\text{u}_y + \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u3092\u78ba\u8a8d\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u6b21\u306e 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5107f1a0b5a49b0ffd79eb20211c48b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (2,3) \\qquad \\vv{\\text{v}}=(4, -1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-24ac65138e4d395f7773aa19ba806a49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} + \\vv{\\text{v}}&amp; =(2,3) +(4,-1) \\\\[2ex] &amp; = (2+4,3+(-1)) \\\\[2ex] &amp; = \\bm{(6,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8868\u793a\u304b\u3089\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u901a\u5e38\u3001\u5e73\u884c\u56db\u8fba\u5f62\u306e\u6cd5\u5247\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u304c\u3001\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001 <a href=\"https:\/\/mathority.org\/ja\/\u30d8\u3099\u30af\u30c8\u30eb\u306e\u5408\u8a08\u3092\u30af\u3099\u30e9\u30d5\u3066\u3099\u6570\u5024\u7684\u306b\u89e3\u304f\u6f14\u7fd2\u554f\u984c\u306e\u8ffd\u52a0\/\">2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u8ffd\u52a0\u3059\u308b\u65b9\u6cd5\u306e<\/a>\u4f8b\u3068\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u3092\u53c2\u7167\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"resta-de-vectores\"><\/span>\u30d9\u30af\u30c8\u30eb\u6e1b\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u89e3\u6790\u7684\u306b\u6e1b\u7b97\u3059\u308b\u306b\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u3092\u6e1b\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e X \u5ea7\u6a19\u306f\u4e92\u3044\u306b\u6e1b\u7b97\u3055\u308c\u3001Y \u5ea7\u6a19\u3068\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c755aca302ff1c1b956ca3d91bac1095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} - \\vv{\\text{v}} = (\\text{u}_x - \\text{v}_x \\ , \\ \\text{u}_y - \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u6b21\u306e 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u6e1b\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e6976699c55e7cb1372aca76313b056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,1) \\qquad \\vv{\\text{v}}=(2, -4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5693a8287adebc3a4553358f8a8b0969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} - \\vv{\\text{v}}&amp; =(3,1) -(2,-4) \\\\[2ex] &amp; = (3-2,1-(-4)) \\\\[2ex]&amp; = (3-2,1+4) \\\\[2ex] &amp; = \\bm{(1,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u52a0\u7b97\u3068\u540c\u69d8\u306b\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u8868\u73fe\u3092\u4f7f\u7528\u3057\u3066\u6e1b\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u306b\u306f\u3001\u901a\u5e38\u306f\u4e09\u89d2\u5b9a\u898f\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u304c\u3001\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u3059\u3079\u3066\u3092\u4f8b\u3068\u3001 <a href=\"https:\/\/mathority.org\/ja\/\u6570\u5024\u7684\u306b\u30d8\u3099\u30af\u30c8\u30eb\u3092\u6e1b\u7b97\u3059\u308b-\u30af\u3099\u30e9\u30d5\u3092\u4f7f\u7528\u3057\u3066\u4f8b\u3092\u89e3\u304f-\u6f14\u7fd2\u554f\u984c\u3092\u6e1b\u7b97\u3059\u308b\/\">2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u6e1b\u7b97\u3059\u308b\u65b9\u6cd5<\/a>\u306b\u95a2\u3059\u308b\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2\u3067\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"modulo-de-un-vector\"><\/span>\u30d9\u30af\u30c8\u30eb\u306e\u30e2\u30b8\u30e5\u30fc\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u3053\u306e\u30da\u30fc\u30b8\u306e\u6700\u521d\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306f\u305d\u306e\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055 (\u307e\u305f\u306f\u5927\u304d\u3055) \u306f\u3001\u305d\u306e\u6210\u5206\u304b\u3089\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4b2f8c9cdb09377a66fbce8392c30ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u5e73\u9762\u5185\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u6b21\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95466c107aed66569925d4b89a3a939b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ \\text{u}_x^2+\\text{u}_y^2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6273ca0b37b024bc5684ec07237607bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d78c0f573a5d2db399d099ebc4a3cb85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =\\sqrt{3^2+(-4)^2} = \\sqrt{9+16}=\\sqrt{25} = \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"316\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u975e\u5e38\u306b\u5358\u7d14\u305d\u3046\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6c7a\u5b9a\u306f\u8907\u96d1\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u591a\u304f\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3001 <a href=\"https:\/\/mathority.org\/ja\/\u30d8\u3099\u30af\u30c8\u30eb\u5f0f\u306e\u30e2\u30b7\u3099\u30e5\u30fc\u30eb\u306e\u4f8b-\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\/\">\u30d9\u30af\u30c8\u30eb\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2<\/a>\u3067\u7df4\u7fd2\u3057\u305f\u3044\u5834\u5408\u306f\u3001\u3053\u306e\u30ea\u30f3\u30af\u3055\u308c\u305f\u30da\u30fc\u30b8\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"multiplicacion-de-un-vector-por-un-escalar\"><\/span>\u30d9\u30af\u30c8\u30eb\u3068\u30b9\u30ab\u30e9\u30fc\u306e\u4e57\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u30d9\u30af\u30c8\u30eb\u3068\u6570\u5024 (\u307e\u305f\u306f\u30b9\u30ab\u30e9\u30fc) \u306e\u7a4d\u3092\u6570\u5024\u7684\u306b\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5404\u6210\u5206\u306b\u305d\u306e\u6570\u5024\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc2018686141332d7620fe51d93dae8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\\\\[4ex]k\\cdot \\vv{\\text{u}} =(k\\cdot \\text{u}_x \\ , \\ k\\cdot \\text{u}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b21\u306e\u4e00\u822c\u7684\u306a\u4f8b\u3067\u306f\u3001\u30b9\u30ab\u30e9\u30fc\u306e\u7b26\u53f7\u306b\u95a2\u4fc2\u306a\u304f\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u304c\u3069\u306e\u3088\u3046\u306b\u7dad\u6301\u3055\u308c\u308b\u304b\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3001\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306b\u4e57\u7b97\u3059\u308b\u6570\u5024\u306e\u7b26\u53f7\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/multiplication-ou-produit-dun-nombre-ou-dun-scalaire-par-un-vecteur.webp\" alt=\"\u6570\u5024\u307e\u305f\u306f\u30b9\u30ab\u30e9\u30fc\u3068\u30d9\u30af\u30c8\u30eb\u306e\u4e57\u7b97\u307e\u305f\u306f\u7a4d\" class=\"wp-image-283\" width=\"298\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4ee5\u4e0b\u306b\u3001\u30d9\u30af\u30c8\u30eb\u3068\u6570\u5024\u306e\u7a4d\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306e\u6570\u5024\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c2dd0a37f737f7c82d6da8b971ca0f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} =(3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87282d0a06c534058bd4b64120bdf391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{\\text{u}} =(4 \\cdot 3 \\ , \\ 4 \\cdot (-2)) = \\bm{(12,-8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-escalar\"><\/span>\u30b9\u30ab\u30e9\u30fc\u7a4d<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u89e3\u6790\u5e7e\u4f55\u5b66\u306b\u304a\u3051\u308b\u30c9\u30c3\u30c8\u7a4d\u306f\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u4e57\u7b97\u3057\u3066\u5b9f\u6570\u306b\u5909\u63db\u3059\u308b\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f09930024fc5c410889bea53d06982e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle  \\vv{\\text{u}} \\cdot \\vv{\\text{v}} = \\text{u}_x\\cdot \\text{v}_x + \\text{u}_y\\cdot \\text{v}_y \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ee5\u4e0b\u306b\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u5185\u7a4d\u306e\u7d50\u679c\u3092\u8a08\u7b97\u3059\u308b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7437bf59c08f823d3a9ca8b5f32a3f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,2) \\qquad \\vv{\\text{v}} = (-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2a8137101f391be2b197764b8b21223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{aligned} \\vv{\\text{u}} \\cdot \\vv{\\text{v}}&amp;=(4,2)\\cdot (-1,3) \\\\[1.5ex]&amp;=4\\cdot (-1) + 2 \\cdot 3 \\\\[1.5ex] &amp; = -4+6  \\\\[1.5ex] &amp; =\\bm{10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u30ea\u30f3\u30af\u3067\u306f\u3001 <a href=\"https:\/\/mathority.org\/ja\/2-\u3064\u306e\u30d8\u3099\u30af\u30c8\u30eb\u306e\u9593\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3092\u8a08\u7b97\u3059\u308b-\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u306e\u4f8b\/\">\u30c9\u30c3\u30c8\u7a4d\u306e\u4ed6\u306e\u4f8b\u3092<\/a>\u53c2\u7167\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u5185\u7a4d\u3092\u6c42\u3081\u308b\u5225\u306e\u65b9\u6cd5\u3001\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u7528\u3057\u305f\u3053\u306e\u30bf\u30a4\u30d7\u306e\u6f14\u7b97\u306e\u7279\u6027\u3001\u304a\u3088\u3073\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3082\u898b\u3064\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-vectorial\"><\/span>\u30d9\u30af\u30c8\u30eb\u7a4d<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u540d\u524d\u306f\u3088\u304f\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u5185\u7a4d\u3068\u5916\u7a4d\u306f\u307e\u3063\u305f\u304f\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u5916\u7a4d<\/strong>(\u5916\u7a4d\u3068\u3082\u547c\u3070\u308c\u308b) \u306f\u3001\u7a7a\u9593 (R3) \u5185\u306e 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3001\u3064\u307e\u308a 3 \u5ea7\u6a19\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6f14\u7b97\u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e 3 \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-581394386a4c68ca2bfa92fb4e2445ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (\\text{u}_x,\\text{u}_y,\\text{u}_z) \\qquad \\vv{\\text{v}}= (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u306f\u3001\u6b21\u306e 3\u00d73 \u884c\u5217\u5f0f\u306e\u7d50\u679c\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c85dc2dfb37842b31dea465c8887bc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\end{vmatrix}  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u30d9\u30af\u30c8\u30eb\u306f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-899f7cb82c85508ac2129e2393976f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}, \\vv{j},\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u3001\u305d\u308c\u305e\u308c X\u3001Y\u3001Z \u8ef8\u65b9\u5411\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u7d50\u679c\u306e\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306f\u3001\u4e57\u7b97\u3055\u308c\u305f 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3054\u60f3\u50cf\u306e\u3068\u304a\u308a\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u6f14\u7b97\u3092\u89e3\u6c7a\u3059\u308b\u306e\u306f\u3053\u308c\u307e\u3067\u306e\u6f14\u7b97\u3088\u308a\u3082\u96e3\u3057\u3044\u305f\u3081\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u5916\u7a4d\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u306b\u3064\u3044\u3066\u306e\u8a73\u7d30\u306a\u8aac\u660e\u3092 1 \u30da\u30fc\u30b8\u5168\u4f53\u306b\u7528\u610f\u3057\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u8208\u5473\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u30a2\u30af\u30bb\u30b9\u3057\u3066\u3001 <a href=\"https:\/\/mathority.org\/ja\/2-\u3064\u306e\u30d8\u3099\u30af\u30c8\u30eb\u306e\u5916\u7a4d-\u30af\u30ed\u30b9\u516c\u5f0f\u306e\u4f8b-\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\/\">\u89e3\u6c7a\u3055\u308c\u305f\u30d9\u30af\u30c8\u30eb\u7a4d\u6f14\u7fd2<\/a>\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-mixto\"><\/span>\u6df7\u5408\u88fd\u54c1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e<strong>\u6df7\u5408\u7a4d<\/strong>(\u30c8\u30ea\u30d7\u30eb \u30c9\u30c3\u30c8\u7a4d\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \u306f\u3001\u30c9\u30c3\u30c8\u7a4d\u3068\u30d9\u30af\u30c8\u30eb\u7a4d\u3068\u3044\u3046 2 \u3064\u306e\u7570\u306a\u308b\u30bf\u30a4\u30d7\u306e\u6f14\u7b97\u3092\u542b\u3080 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u9023\u7d9a\u4e57\u7b97\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3068\u30b9\u30ab\u30e9\u30fc (\u5b9f\u6570) \u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u6df7\u5408\u7a4d\u306f 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30d9\u30af\u30c8\u30eb\u7a4d\u3092\u8a08\u7b97\u3057\u3001\u305d\u306e\u5f8c\u3001\u5f97\u3089\u308c\u305f\u7d50\u679c\u306b 3 \u756a\u76ee\u306e\u30d9\u30af\u30c8\u30eb\u3092\u30d9\u30af\u30c8\u30eb\u4e57\u7b97\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u5f0f\u3092\u898b\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20bc6ca73caab65fbe6dafc458258ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.3pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}}) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u30d9\u30af\u30c8\u30eb\u7a4d\u3068\u540c\u69d8\u306b\u3001\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6df7\u5408\u7a4d\u3092\u89e3\u304f\u306e\u306f\u7c21\u5358\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u305f\u3081\u3001 <a href=\"https:\/\/mathority.org\/ja\/3-\u3064\u306e\u30d8\u3099\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u307e\u305f\u306f-3-\u3064\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u306e\u4f8b\/\">3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d<\/a>\u306b\u95a2\u3059\u308b\u3053\u306e\u8aac\u660e\u3092\u53c2\u7167\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u3053\u306e\u8aac\u660e\u306b\u306f\u3001\u4f8b\u3001\u89e3\u6c7a\u6e08\u307f\u306e\u6f14\u7fd2\u3001\u304a\u3088\u3073\u3053\u306e\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u306e\u5e7e\u4f55\u5b66\u7684\u610f\u5473\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-vectores\"><\/span>\u30d9\u30af\u30c8\u30eb\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d9\u30af\u30c8\u30eb\u306b\u306f\u3055\u307e\u3056\u307e\u306a\u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u77e5\u3063\u3066\u304a\u304f\u3079\u304d\u6700\u3082\u91cd\u8981\u306a\u5b9a\u7fa9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li><strong>\u5358\u4f4d\u30d9\u30af\u30c8\u30eb<\/strong>: \u30e2\u30b8\u30e5\u30fc\u30eb\u304c 1 \u306b\u7b49\u3057\u3044\u30d9\u30af\u30c8\u30eb\u3002<\/li>\n<li><strong>\u56fa\u5b9a\u30d9\u30af\u30c8\u30eb<\/strong>: \u30d9\u30af\u30c8\u30eb\u306e\u539f\u70b9\u3092\u56fa\u5b9a\u70b9\u306b\u9069\u7528\u3059\u308b\u3068\u3001\u30d9\u30af\u30c8\u30eb\u306f\u56fa\u5b9a\u3055\u308c\u307e\u3059\u3002<\/li>\n<li><strong>\u81ea\u7531\u30d9\u30af\u30c8\u30eb<\/strong>: \u30d9\u30af\u30c8\u30eb\u306f\u3001\u9069\u7528\u70b9\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u306f\u81ea\u7531\u3067\u3059\u304c\u3001\u81ea\u7531\u70b9\u3067\u3059\u3002<\/li>\n<li><strong>\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u4f5c\u7528\u7dda (\u30d9\u30af\u30c8\u30eb\u304c\u4f4d\u7f6e\u3059\u308b\u76f4\u7dda) \u3092\u5171\u6709\u3059\u308b\u5834\u5408\u3001\u305d\u308c\u3089\u306e\u30d9\u30af\u30c8\u30eb\u306f\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u7b49\u4fa1\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u30b5\u30a4\u30ba\u3001\u540c\u3058\u610f\u5473\u3001\u540c\u3058\u65b9\u5411\u3092\u6301\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3089\u306e\u30d9\u30af\u30c8\u30eb\u306f\u7b49\u82b1\u7c89\u3067\u3059 (\u305f\u3060\u3057\u3001\u9069\u7528\u70b9\u304c\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059)\u3002<\/li>\n<li><strong>\u9023\u7d50\u30d9\u30af\u30c8\u30eb<\/strong>: \u9023\u7d50\u30d9\u30af\u30c8\u30eb\u306f\u3001\u540c\u3058\u7dda\u4e0a\u3067\u4f5c\u7528\u3059\u308b\u7b49\u82b1\u7c89\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/li>\n<li><strong>\u53cd\u5bfe\u306e\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u5927\u304d\u3055\u3068\u65b9\u5411\u304c\u540c\u3058\u3067\u65b9\u5411\u304c\u7570\u306a\u308b\u5834\u5408\u3001\u53cd\u5bfe\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/strong>: \u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u70b9 (0,0) (\u5ea7\u6a19\u306e\u539f\u70b9) \u3092\u539f\u70b9\u3068\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/li>\n<li><strong>\u7af6\u5408\u3059\u308b\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u305d\u306e\u4f5c\u7528\u7dda\u304c\u540c\u3058\u70b9\u3092\u901a\u904e\u3059\u308b\u3001\u3064\u307e\u308a\u4ea4\u5dee\u3059\u308b\u3068\u304d\u306b\u540c\u6642\u306b\u5b58\u5728\u3057\u307e\u3059\u3002<\/li>\n<li><strong>\u5e73\u884c\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u305d\u306e\u65b9\u5411\u306b\u95a2\u4fc2\u306a\u304f\u3001\u540c\u3058\u65b9\u5411\u3067\u3042\u308c\u3070\u5e73\u884c\u3067\u3059\u3002<\/li>\n<li><strong>\u5782\u76f4\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u304c 90 \u5ea6\u306e\u89d2\u5ea6\u3092\u5f62\u6210\u3059\u308b\u5834\u5408\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u5782\u76f4 (\u307e\u305f\u306f\u76f4\u4ea4) \u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u6b63\u898f\u76f4\u4ea4\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u304c\u4e92\u3044\u306b\u5782\u76f4\u3067\u3042\u308a\u3001\u3055\u3089\u306b\u30e6\u30cb\u30bf\u30ea\u3067\u3042\u308b (\u5927\u304d\u3055\u304c 1 \u306b\u7b49\u3057\u3044) \u5834\u5408\u3001\u305d\u308c\u3089\u306e\u30d9\u30af\u30c8\u30eb\u306f\u6b63\u898f\u76f4\u4ea4\u3067\u3059\u3002<\/li>\n<li>\u540c\u4e00\u5e73\u9762<strong>\u4e0a\u306b\u3042\u308b\u30d9\u30af\u30c8\u30eb<\/strong>: 2 \u3064\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u5e73\u9762\u5185\u306b\u542b\u307e\u308c\u308b\u5834\u5408\u3001\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"angulo-entre-dos-vectores\"><\/span> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u89d2\u5ea6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u5b9a\u3055\u308c\u305f 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u9593\u306e\u89d2\u5ea6\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u6b21\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67007d32353dedf96eb6b965b16c5489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4501274336c637b37c6332eae5c6c229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u305d\u3057\u3066<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a59cd4f2581db3318d38a2a77340a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u305d\u3057\u3066<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u305d\u308c\u305e\u308c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u304b\u3001\u305d\u306e\u7279\u5fb4\u3001\u8a08\u7b97\u65b9\u6cd5\u3001\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u305f\u6f14\u7b97\u306e\u65b9\u6cd5\u3001\u5b58\u5728\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u30bf\u30a4\u30d7\u306a\u3069\u3001\u30d9\u30af\u30c8\u30eb\u306b\u95a2\u3059\u308b\u3059\u3079\u3066\u3092\u8aac\u660e\u3057\u307e\u3059\u3002 \u30d9\u30af\u30c8\u30eb\u3068\u306f\u4f55\u3067\u3059\u304b? \u30d9\u30af\u30c8\u30eb\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u6570\u5b66\u3067 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%a8%e3%81%af%e4%bd%95%e3%81%a7%e3%81%99%e3%81%8b-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86%e5%ad%a6%e3%81%ae%e4%be%8b\/\"> <span class=\"screen-reader-text\">\u30d9\u30af\u30c8\u30eb\uff08\u6570\u5b66\uff09\u3068\u306f\u4f55\u3067\u3059\u304b?<\/span> \u3082\u3063\u3068\u8aad\u3080 &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":[21],"tags":[],"class_list":["post-268","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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