{"id":215,"date":"2023-07-11T12:27:22","date_gmt":"2023-07-11T12:27:22","guid":{"rendered":"https:\/\/mathority.org\/ja\/3-%e3%81%a4%e3%81%ae%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%b7%b7%e5%90%88%e7%a9%8d%e3%81%be%e3%81%9f%e3%81%af-3-%e3%81%a4%e3%81%ae%e3%82%b9%e3%82%ab%e3%83%a9%e3%83%bc%e7%a9%8d%e3%81%ae\/"},"modified":"2023-07-11T12:27:22","modified_gmt":"2023-07-11T12:27:22","slug":"3-%e3%81%a4%e3%81%ae%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%b7%b7%e5%90%88%e7%a9%8d%e3%81%be%e3%81%9f%e3%81%af-3-%e3%81%a4%e3%81%ae%e3%82%b9%e3%82%ab%e3%83%a9%e3%83%bc%e7%a9%8d%e3%81%ae","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/3-%e3%81%a4%e3%81%ae%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%b7%b7%e5%90%88%e7%a9%8d%e3%81%be%e3%81%9f%e3%81%af-3-%e3%81%a4%e3%81%ae%e3%82%b9%e3%82%ab%e3%83%a9%e3%83%bc%e7%a9%8d%e3%81%ae\/","title":{"rendered":"3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d (\u307e\u305f\u306f\u4e09\u91cd\u70b9\u7a4d)"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u30013 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d (\u307e\u305f\u306f\u4e09\u91cd\u70b9\u7a4d) \u3068\u306f\u4f55\u304b\u3001\u304a\u3088\u3073\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6f14\u7b97\u306b\u95a2\u3059\u308b\u4f8b\u3001\u6f14\u7fd2\u3001\u304a\u3088\u3073\u89e3\u6c7a\u3055\u308c\u305f\u554f\u984c\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u6df7\u5408\u88fd\u54c1\u306e\u7279\u6027\u3068\u7528\u9014\u3082\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-producto-mixto-de-tres-vectores\"><\/span> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e<strong>\u6df7\u5408\u7a4d<\/strong>(<strong>\u30c8\u30ea\u30d7\u30eb \u30c9\u30c3\u30c8\u7a4d<\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \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<\/a>\u3068<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\/\">\u30d9\u30af\u30c8\u30eb\u7a4d<\/a>\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\u3053\u306e\u3088\u3046\u306b\u66f8\u304f\u3068\u975e\u5e38\u306b\u8907\u96d1\u306b\u898b\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u5b9f\u969b\u306b\u306f\u305d\u308c\u307b\u3069\u8907\u96d1\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4e09\u91cd\u70b9\u7a4d\u306e\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-7904652c5b12243a6dc713936dba9d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}})\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u305d\u306e\u5f0f\u304b\u3089\u5206\u304b\u308b\u3088\u3046\u306b\u30013 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306f 2 \u3064\u306e\u89d2\u62ec\u5f27\u3067\u793a\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-calcular-el-producto-mixto-de-tres-vectores\"><\/span> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e09\u91cd\u30c9\u30c3\u30c8\u7a4d\u306e\u516c\u5f0f\u306f\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u8aac\u660e\u3057\u305f\u3082\u306e\u3067\u3059\u304c\u3001\u3088\u308a\u7c21\u5358\u3067\u9ad8\u901f\u306a\u5225\u306e\u65b9\u6cd5\u304c\u3042\u308b\u305f\u3081\u3001\u4e00\u822c\u7684\u306b\u306f 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u306f\u4f7f\u7528\u3055\u308c\u307e\u305b\u3093\u3002 <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u4efb\u610f\u306e 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u6b21\u306e\u3088\u3046\u306b\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-3d0daa4c1f9e1aff4f64a39f229bc207_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)\\qquad \\vv{\\text{w}}= (\\text{w}_x,\\text{w}_y,\\text{w}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"431\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6df7\u5408\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001<\/strong>\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b 3\u00d73 \u884c\u5217\u5f0f\u3092\u89e3\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-a3fed933d4d02bb5ca6f5bae06ea544d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]=\\begin{vmatrix} \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\\\[1.1ex] \\text{w}_x &amp; \\text{w}_y &amp; \\text{w}_z \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"188\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p><span style=\"text-decoration: underline;\">\u3053\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u306e\u4f8b\u3092<\/span>\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6b21\u306e 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u304c\u6c42\u3081\u3089\u308c\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-d90f4dd611d93b46a9001a7fe26e03f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (1,2,0) \\qquad \\vv{\\text{v}}= (0,-1,3)\\qquad \\vv{\\text{w}}= (-2,4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"369\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6df7\u5408\u7a4d\u3092\u6c7a\u5b9a\u3059\u308b\u306b\u306f\u3001\u884c\u5217\u306e\u884c\u306b\u30d9\u30af\u30c8\u30eb\u3092\u914d\u7f6e\u3057\u3066\u6b21\u6570 3 \u306e\u884c\u5217\u5f0f\u3092\u69cb\u7bc9\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-e5341b4a39b42c1284a4b0129b38b61a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]=\\begin{vmatrix} 1 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp; 4 &amp; 1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"180\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u884c\u5217\u306e\u884c\u5217\u5f0f\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308b\u3060\u3051\u3067\u3059\u3002\u3053\u308c\u306b\u306f\u4efb\u610f\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001Sarrus \u306e\u6cd5\u5247\u3092\u9069\u7528\u3057\u307e\u3059 (\u305f\u3060\u3057\u3001\u3053\u308c\u306f\u52a0\u7b97\u307e\u305f\u306f\u4f59\u56e0\u5b50\u306b\u3088\u3063\u3066\u3082\u5b9f\u884c\u3067\u304d\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-df86565048cf897265878936f2294525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 1 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp; 4 &amp; 1 \\end{vmatrix} \\\\[2ex] &amp;= -1-12+0-0-12-0 \\\\[2ex] &amp; = \\bm{-25} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"276\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<hr class=\"wp-block-separator has-text-color has-background has-pale-cyan-blue-background-color has-pale-cyan-blue-color is-style-wide\">\n<p> 2 \u3064\u306e\u624b\u9806\u304c\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u306b\u3001\u6b21\u306e\u5b9a\u7fa9\u306b\u5f93\u3063\u3066\u540c\u3058\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\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-e4d15d610ca9b4cb39e9f268cfb152ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] &amp; = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}})\\\\[2ex] &amp;=(1,2,0) \\cdot \\Bigl( (0,-1,3)\\times (-2,4,1)\\Bigr) \\\\[2ex] &amp; = (1,2,0) \\cdot \\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 0&amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp;4&amp;1 \\end{vmatrix} \\\\[2ex] &amp;=  (1,2,0) \\cdot (-13,-6,-2) \\\\[2ex] &amp; = \\bm{-25} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"262\" width=\"332\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u884c\u5217\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6df7\u5408\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u9ad8\u901f\u3067\u9593\u9055\u3044\u3092\u72af\u3059\u53ef\u80fd\u6027\u304c\u4f4e\u3044\u305f\u3081\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3082\u7d50\u679c\u306f\u540c\u3058\u306a\u306e\u3067\u3001\u304a\u597d\u307f\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \ud83d\udc4d <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-geometrica-del-producto-mixto\"><\/span>\u6df7\u5408\u7a4d\u306e\u5e7e\u4f55\u5b66\u7684\u89e3\u91c8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u304c\u308f\u304b\u308b\u3068\u3001\u6df7\u5408\u7a4d\u306f\u4f55\u306e\u305f\u3081\u306b\u3042\u308b\u306e\u304b\u7591\u554f\u306b\u601d\u3046\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u6570\u5b66\u3067\u306f\u3001\u5e73\u884c\u516d\u9762\u4f53\u306e\u4f53\u7a4d\u3068\u56db\u9762\u4f53\u306e\u4f53\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u3044\u3046 2 \u3064\u306e\u4e3b\u306a\u7528\u9014\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u5e73\u884c\u516d\u9762\u4f53\u306e\u4f53\u7a4d\u306f\u3001<\/strong>\u5e7e\u4f55\u5b66\u7684\u30d5\u30a3\u30fc\u30eb\u30c9\u306e 3 \u6b21\u5143\u3092\u30de\u30fc\u30af\u3059\u308b\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306e\u7d76\u5bfe\u5024\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-produit-mixte-de-trois-vecteurs.webp\" alt=\"3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u307e\u305f\u306f 3 \u3064\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u306e\u4f8b\" class=\"wp-image-999\" width=\"309\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6df7\u5408\u7a4d\u306e\u5225\u306e\u7528\u9014\u306f\u3001<strong>\u56db\u9762\u4f53\u306e\u4f53\u7a4d<\/strong>\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u5e7e\u4f55\u5b66\u7684\u306b\u306f\u3001\u6df7\u5408\u7a4d\u306e\u7d76\u5bfe\u5024\u306e 6 \u756a\u76ee\u306e\u90e8\u5206\u306f\u56db\u9762\u4f53\u306e\u4f53\u7a4d\u3092\u8868\u3059\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-mixte-de-trois-vecteurs-dans-r3.webp\" alt=\"r3 \u306e 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\" class=\"wp-image-1002\" width=\"273\" height=\"327\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-producto-mixto-o-triple-producto-escalar\"><\/span>\u6df7\u5408\u7a4d\u307e\u305f\u306f\u30c8\u30ea\u30d7\u30eb\u30c9\u30c3\u30c8\u7a4d\u306e\u7279\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6df7\u5408\u7a4d\u3001\u3064\u307e\u308a\u30c8\u30ea\u30d7\u30eb \u30b9\u30ab\u30e9\u30fc\u7a4d\u306b\u306f\u3001\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u4e00\u822c\u306b\u3001\u6df7\u5408\u7a4d\u30d9\u30af\u30c8\u30eb\u306e<strong>\u9806\u5e8f<\/strong>\u306e\u5909\u5316\u306f\u3001\u7b26\u53f7\u306e\u5909\u5316\u3082\u610f\u5473\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6df7\u5408\u7a4d\u30d9\u30af\u30c8\u30eb\u306e\u9806\u5e8f\u304c\u91cd\u8981\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ce0eff894cd1fa149c6d8c8ae6f0f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = -\\bigl[\\vv{\\text{v}},\\vv{\\text{u}},\\vv{\\text{w}}\\bigr] = -\\bigl[\\vv{\\text{u}},\\vv{\\text{w}},\\vv{\\text{v}}\\bigr] = - \\bigl[\\vv{\\text{w}},\\vv{\\text{v}},\\vv{\\text{u}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"356\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li>\u305f\u3060\u3057\u3001\u9806\u5e8f\u3092<strong>\u5468\u671f\u7684\u306b<\/strong>\u5909\u66f4\u3057\u3066\u3082\u3001\u7b26\u53f7\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e3f514d940b6d366613f59c6cd8bbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\bigl[\\vv{\\text{v}},\\vv{\\text{w}},\\vv{\\text{u}}\\bigr] = \\bigl[\\vv{\\text{w}},\\vv{\\text{u}},\\vv{\\text{v}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"229\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> 3 \u6b21\u5143\u7a7a\u9593 (R3 \u5185) \u3067\u306f\u3001(\u540c\u3058\u5e73\u9762\u306b\u5c5e\u3059\u308b) 3 \u3064\u306e<strong>\u7dda\u5f62\u4f9d\u5b58<\/strong>\u30d9\u30af\u30c8\u30eb\u307e\u305f\u306f<strong>\u5171\u9762\u30d9\u30af\u30c8\u30eb<\/strong>\u306e\u6df7\u5408\u7a4d\u306f 0 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-productos-mixtos\"><\/span>\u6df7\u5408\u88fd\u54c1\u306e\u554f\u984c\u3092\u4fee\u6b63<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408:<\/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-e4ea59160804c0287d02cbd1cf01b787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,-1,2) \\qquad \\vv{\\text{v}}= (-2,0,1)\\qquad \\vv{\\text{w}}= (5,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\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-6f6a0d080e09991ca4dc57ff1dd1ab83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u305d\u306e\u6df7\u5408\u7a4d\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19\u3067\u69cb\u6210\u3055\u308c\u308b\u884c\u5217\u5f0f\u3092\u89e3\u304f\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-549ed90889d541ae4a1075449567b062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 3 &amp; -1 &amp; 2 \\\\[1.1ex] -2 &amp; 0 &amp; 1 \\\\[1.1ex] 5 &amp; 1 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= 0-5-4-0-3+2 \\\\[2ex] &amp; = \\bm{-10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408:<\/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-269e213cd1d1e52c2189fe0dc420f93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (7,2,-3) \\qquad \\vv{\\text{v}}= (2,4,9)\\qquad \\vv{\\text{w}}= (4,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"369\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6df7\u5408\u7a4d\u3092\u6c7a\u5b9a\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-6f6a0d080e09991ca4dc57ff1dd1ab83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u305d\u306e\u6df7\u5408\u7a4d\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u7dda\u5f62\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u3092\u6301\u3064\u884c\u5217\u5f0f\u3092\u89e3\u304f\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-29b46155243552a99f6fd75de69f59da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 7 &amp; 2 &amp; -3 \\\\[1.1ex] 2 &amp; 4 &amp; 9 \\\\[1.1ex] 4 &amp; 3 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= -28+72-18+48-189+4 \\\\[2ex] &amp; = \\bm{-111} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"312\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p> 3 \u8fba\u304c\u6b21\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u76f4\u65b9\u4f53\u306e\u4f53\u7a4d\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-897316aad94e2c06a745cc34bdcd2cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (0,2,5) \\qquad \\vv{\\text{v}}= (-1,6,2)\\qquad \\vv{\\text{w}}= (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u76f4\u65b9\u4f53\u306e\u4f53\u7a4d\u306f\u3001\u8fba\u3068\u3057\u3066\u6301\u3064 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306e\u7d76\u5bfe\u5024\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u30d9\u30af\u30c8\u30eb\u306e\u4e09\u91cd\u5916\u7a4d\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-9718b369a508216fbb69ab68ac7de381_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 0 &amp; 2 &amp; 5 \\\\[1.1ex] -1 &amp; 6 &amp; 2 \\\\[1.1ex] 3 &amp; 1 &amp; 2 \\end{vmatrix} \\\\[2ex] &amp;= 0+12-5-90-0+4 \\\\[2ex] &amp; = -79 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u76f4\u65b9\u4f53\u306e\u4f53\u7a4d\u306f\u6df7\u5408\u7a4d\u306e\u7d50\u679c\u306e\u7d76\u5bfe\u5024\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-6074917d7c095bd718364a5ed3081c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\lvert -79 \\rvert = \\bm{79}\\ \\mathbf{u}\\bm{^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"145\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p>\u6b21\u306e\u70b9\u3092\u9802\u70b9\u3068\u3059\u308b\u56db\u9762\u4f53\u306e\u4f53\u7a4d\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-4c798eaa40f98c461a076a2bc0aa0910_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,0,2) \\qquad B(3,3,2)\\qquad C(5,-1,4)\\qquad D(4,2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"401\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u56db\u9762\u4f53\u306e\u30a8\u30c3\u30b8\u3092\u8868\u3059\u30d9\u30af\u30c8\u30eb\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-fe16cd346a46022ffcd90ad080b305ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A= (3,3,2)-(1,0,2)=(2,3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"337\" 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-7bb115ce61905a3f3a5c76dfd152b8f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC}=C-A= (5,-1,4)-(1,0,2)=(4,-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" 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-11697d137db244fd5b7a5f6328181183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD}=D-A= (4,2,1)-(1,0,2)=(3,2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"353\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56db\u9762\u4f53\u306e\u4f53\u7a4d\u306f\u3001\u56db\u9762\u4f53\u306e\u30a8\u30c3\u30b8\u306b\u5bfe\u3057\u3066\u6301\u3064 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306e\u7d76\u5bfe\u5024\u306e 1\/6 \u306b\u76f8\u5f53\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u3001\u898b\u3064\u304b\u3063\u305f\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\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-d384e76415a756b834e0a8e7c695b1c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 2 &amp; 3 &amp; 0 \\\\[1.1ex] 4 &amp; -1 &amp; 2 \\\\[1.1ex] 3 &amp; 2 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= 2+18+0-0-8+12 \\\\[2ex] &amp; = 24 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"262\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u56db\u9762\u4f53\u306e\u4f53\u7a4d\u306f\u3001\u6df7\u5408\u7a4d\u306e\u7d76\u5bfe\u5024\u306e 6 \u5206\u306e 1 \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-0e1aefc732626b5a6d55a904d03452b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\cfrac{1}{6} \\cdot \\lvert 24 \\rvert = \\cfrac{24}{6} = \\bm{4} \\ \\mathbf{u}\\bm{^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"189\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u30013 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d (\u307e\u305f\u306f\u4e09\u91cd\u70b9\u7a4d) \u3068\u306f\u4f55\u304b\u3001\u304a\u3088\u3073\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u6f14\u7b97\u306b\u95a2\u3059\u308b\u4f8b\u3001\u6f14\u7fd2\u3001\u304a\u3088\u3073\u89e3\u6c7a\u3055\u308c\u305f\u554f\u984c\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u6df7\u5408\u88fd\u54c1\u306e\u7279\u6027\u3068\u7528\u9014 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/3-%e3%81%a4%e3%81%ae%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%b7%b7%e5%90%88%e7%a9%8d%e3%81%be%e3%81%9f%e3%81%af-3-%e3%81%a4%e3%81%ae%e3%82%b9%e3%82%ab%e3%83%a9%e3%83%bc%e7%a9%8d%e3%81%ae\/\"> <span class=\"screen-reader-text\">3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d (\u307e\u305f\u306f\u4e09\u91cd\u70b9\u7a4d)<\/span> \u3082\u3063\u3068\u8aad\u3080 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