{"id":250,"date":"2023-07-10T11:53:09","date_gmt":"2023-07-10T11:53:09","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%bc%8f-r3-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b-2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%a7%92%e5%ba%a6\/"},"modified":"2023-07-10T11:53:09","modified_gmt":"2023-07-10T11:53:09","slug":"%e7%a9%ba%e9%96%93%e5%bc%8f-r3-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b-2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%a7%92%e5%ba%a6","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%bc%8f-r3-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b-2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%a7%92%e5%ba%a6\/","title":{"rendered":"\u7a7a\u9593\u5185\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6 (\u5f0f)"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u7a7a\u9593\u5185\u306e 2 \u3064\u306e\u5e73\u9762\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 (\u516c\u5f0f) \u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u984c\u3092\u898b\u3066\u3001\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-dos-planos\"><\/span> 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\uff12\u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306f\u3001\u524d\u8a18\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u306b\u7b49\u3057\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u305d\u308c\u3089\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u7b49\u3057\u3044\u305f\u3081\u3001\u305d\u308c\u3089\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u304c\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/strong> <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u304c\u6b63\u78ba\u306b\u308f\u304b\u3063\u305f\u3089\u3001\u7a7a\u9593 (R3) \u5185\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306f\u3001 <a href=\"https:\/\/mathority.org\/ja\/2-\u3064\u306e\u30d8\u3099\u30af\u30c8\u30eb\u306e\u9593\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306e\u4f8b\u3068\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\/\">2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u89d2\u5ea6\u306e\u516c\u5f0f<\/a>\u304b\u3089\u63a8\u5b9a\u3055\u308c\u307e\u3059\u3002 <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> 2 \u3064\u306e\u7570\u306a\u308b\u5e73\u9762\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u306e) \u65b9\u7a0b\u5f0f\u3092\u8003\u3048\u308b\u3068\u3001\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-dfa3d7e6f1ece8353327be7c9227d75b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ A_1x+B_1y+C_1z+D_1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/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-2c3966346685421fe3e535cf57a5491d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A_2x+B_2y+C_2z+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f\u6b21\u306e\u3068\u304a\u308a\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-eb0ca06882e0d61d6f8134368946ef29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1=(A_1,B_1,C_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" 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-22fba6a063a544bdf257e64d8d139238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2=(A_2,B_2,C_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u3053\u308c\u3089 2 \u3064\u306e\u5e73\u9762\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u6c7a\u5b9a\u3059\u308b\u306b\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\/\">2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d<\/a>\u306e\u8a08\u7b97\u3092\u30de\u30b9\u30bf\u30fc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u305f\u304b\u3092\u899a\u3048\u3066\u3044\u306a\u3044\u5834\u5408\u306f\u3001\u30ea\u30f3\u30af\u306b 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u5185\u7a4d\u3092\u89e3\u304f\u624b\u9806\u304c\u8a18\u8f09\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u984c\u3084\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u30012 \u3064\u306e\u5e73\u9762\u304c\u5782\u76f4\u307e\u305f\u306f\u5e73\u884c\u3067\u3042\u308b\u5834\u5408\u306f\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u76f4\u63a5\u6c7a\u5b9a\u3067\u304d\u308b\u305f\u3081\u3001\u6b21\u306e\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<ul>\n<li> 2 \u3064\u306e<strong>\u5e73\u884c\u306a\u5e73\u9762\u9593<\/strong>\u306e\u89d2\u5ea6\u306f\u3001\u305d\u308c\u3089\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u65b9\u5411\u3092\u6301\u3063\u3066\u3044\u308b\u305f\u3081 0\u00b0 \u3067\u3059\u3002<\/li>\n<li> 2 \u3064\u306e<strong>\u5782\u76f4\u306a\u5e73\u9762<\/strong>\u9593\u306e\u89d2\u5ea6\u306f 90 \u5ea6\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u308c\u3089\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3082\u4e92\u3044\u306b\u5782\u76f4 (\u307e\u305f\u306f\u76f4\u4ea4) \u3057\u3066\u304a\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u76f4\u89d2\u3092\u5f62\u6210\u3059\u308b\u305f\u3081\u3067\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-angulo-entre-dos-planos\"><\/span> 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u3053\u3053\u3067\u306f\u30012 \u3064\u306e\u7570\u306a\u308b\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u6c7a\u5b9a\u3059\u308b\u65b9\u6cd5\u3092\u78ba\u8a8d\u3067\u304d\u308b\u5177\u4f53\u7684\u306a\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u6b21\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3057\u307e\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-60b094e253552cbfa84175e60ef18801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-5y+z+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\"><\/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-364b525ebfd0b5ef85128562d1641cb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 4x+2y+3z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6700\u521d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u306e\u306f\u3001\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19 X\u3001Y\u3001Z \u306f\u3001\u305d\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u306e) \u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 A\u3001B\u3001C \u3068\u305d\u308c\u305e\u308c\u4e00\u81f4\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-17c8988d3ee87dd9e708e46aadbb9086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (3,-5,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-5783f55ed327128d1da574f38c8336e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (4,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3089\u306e\u5e73\u9762\u304c\u5f62\u6210\u3059\u308b\u89d2\u5ea6\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u898b\u3064\u3051\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-96718e6e72f0f3045ee39364f636b419_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+(-5)^2+1^2}= \\sqrt{9+25+1} = \\sqrt{35}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/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-e3558cfa79b7113b469df5b36e00f1ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4^2+2^2+3^2}= \\sqrt{16+4+9} = \\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"280\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u672a\u77e5\u306e\u5024\u3092\u5f0f\u306b\u4ee3\u5165\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-5cdc9e54b22394cf29f35c6c26ee1308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (3,-5,1) \\cdot (4,2,3)\\rvert}{\\sqrt{35} \\cdot \\sqrt{29} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u89e3\u304f\u3053\u3068\u3067\u89d2\u5ea6\u306e\u4f59\u5f26\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-b1923cb6ac441ba0e980bc984bc4804b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 3\\cdot 4 + (-5)\\cdot 2 +1 \\cdot 3 \\rvert}{\\sqrt{35}\\cdot \\sqrt{29} }=\\cfrac{\\lvert 12-10+3 \\rvert}{\\sqrt{1015}}= \\cfrac{5}{31,86}=0,16\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"497\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u96fb\u5353\u3092\u4f7f\u7528\u3057\u3066\u30b3\u30b5\u30a4\u30f3\u306e\u9006\u95a2\u6570\u3092\u5b9f\u884c\u3057\u3066\u89d2\u5ea6\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-57297e96c6a14eed6ff87abfe7699df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,16)=\\bm{80,97\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-angulo-entre-dos-planos\"><\/span> 2\u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u6c42\u3081\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-ac5eb1f4c801eae9ea93342c56e7aa60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+2z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"151\" style=\"vertical-align: -3px;\"><\/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-f7b262c6e50b562858b1c5043548ba75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+y-4z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\"><\/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\">\u6700\u521d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u306e\u306f\u3001\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19 X\u3001Y\u3001Z \u306f\u3001\u305d\u308c\u305e\u308c\u3001\u305d\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u306e) \u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 A\u3001B\u3001\u304a\u3088\u3073 C \u3068\u7b49\u4fa1\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-ef6a043fab595442ed8b17da7798fc34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (1,0,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-158dadd8329a3954114f9d99160e9800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (3,1,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3089\u306e\u5e73\u9762\u304c\u5f62\u6210\u3059\u308b\u89d2\u5ea6\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u898b\u3064\u3051\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-303393672cb4ca6c891bfcf49d3e30b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{1^2+0^2+2^2}= \\sqrt{1+4} = \\sqrt{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -3px;\"><\/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-ede42afce2c7b11dd96617df978ee401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+1^2+(-4)^2}= \\sqrt{9+1+16} = \\sqrt{26}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u308c\u305e\u308c\u306e\u672a\u77e5\u306e\u5024\u3092\u5f0f\u306b\u4ee3\u5165\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-90594e9bdf100d52e0221a86d0878d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (1,0,2) \\cdot (3,1,-4)\\rvert}{\\sqrt{5} \\cdot \\sqrt{26} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u89d2\u5ea6\u306e\u4f59\u5f26\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-fb411278d0746c45c8ef0490e51862b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 1\\cdot 3 + 0\\cdot 1 +2 \\cdot (-4) \\rvert}{\\sqrt{5}\\cdot \\sqrt{26} }=\\cfrac{\\lvert 3-8 \\rvert}{\\sqrt{130}}= \\cfrac{5}{11,4}=0,44\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"440\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u5f8c\u306b\u3001\u96fb\u5353\u3067\u30b3\u30b5\u30a4\u30f3\u3092\u53cd\u8ee2\u3057\u3066 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u6c42\u3081\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-aa9117c27a8c072f275a8cb5fac99528_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,44)=\\bm{63,99\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" 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 2<\/h3>\n<p>\u6b21\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306f\u3044\u304f\u3089\u3067\u3059\u304b? <\/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-7566850c5f664f60ba826bb1ffbf7a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-2y+5z=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"170\" style=\"vertical-align: -4px;\"><\/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-ead661dfbeded4be15602ccda3f2864c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 6x+3y-z-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\"><\/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\">\u6700\u521d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u306e\u306f\u3001\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u306e X\u3001Y\u3001Z \u5ea7\u6a19\u306f\u305d\u308c\u305e\u308c\u3001\u305d\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u7684\u306a) \u65b9\u7a0b\u5f0f\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc A\u3001B\u3001C \u306b\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-54788d8fdba6722dc87ae3c06c350400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (3,-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-f6dee74c50bac2e8859c3f4a3c9742f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (6,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3089\u306e\u5e73\u9762\u304c\u5f62\u6210\u3059\u308b\u89d2\u5ea6\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u898b\u3064\u3051\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-06daed2734e23937ffc63d52314656ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+(-2)^2+5^2}= \\sqrt{9+4+25} = \\sqrt{38}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/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-0f0bafe4966148f6e199dbd2bdc7ede1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{6^2+3^2+(-1)^2}= \\sqrt{36+9+1} = \\sqrt{46}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5404\u5909\u6570\u306e\u5024\u3092\u5f0f\u306b\u4ee3\u5165\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-3d635cbe5718a970df439157ca6346cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (3,-2,5) \\cdot (6,3,-1)\\rvert}{\\sqrt{38} \\cdot \\sqrt{46} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"332\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u89d2\u5ea6\u306e\u4f59\u5f26\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-a24e1ac8ad5f23b1d0734a564fa92a90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 3\\cdot 6 + (-2)\\cdot 3 +5 \\cdot (-1) \\rvert}{\\sqrt{38}\\cdot \\sqrt{46} }=\\cfrac{\\lvert 18-6-5 \\rvert}{\\sqrt{1748}}= \\cfrac{7}{41,81}=0,17\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"516\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u8a08\u7b97\u6a5f\u3067\u30b3\u30b5\u30a4\u30f3\u3092\u53cd\u8ee2\u3057\u3066\u89d2\u5ea6\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-d8fddc88af864b95ff37c56b126af7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,17)=\\bm{80,36\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" 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 3<\/h3>\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u306e\u8a08\u7b97<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6b21\u306e 2 \u3064\u306e\u5e73\u9762\u304c\u5782\u76f4\u306b\u306a\u308b\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-faed0ccf5807a84f20057b0128bbcee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+2y-3z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\"><\/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-9872d7160fb07e1a3ca43e18e24b3435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -2x+5y+kz+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"215\" style=\"vertical-align: -4px;\"><\/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\u7b2c\u4e00\u306b\u3001\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u5e38\u306b\u5404\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u898b\u3064\u3051\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-add7176bfadc88b0c27dd09e33b340cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (1,2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-a3f04e685fb9ce2300340f149aa93059_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (-2,5,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> 2 \u3064\u306e\u5782\u76f4\u306a\u5e73\u9762\u306f 90 \u5ea6\u306e\u89d2\u5ea6\u3092\u306a\u3059\u305f\u3081\u3001\u305d\u308c\u3089\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3082 90 \u5ea6\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u672a\u77e5\u306e\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u304c\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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306e\u89d2\u5ea6\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/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-a35dde3971efe5cdf36340847dcb02e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(90\u00ba) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"151\" style=\"vertical-align: -17px;\"><\/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-eb4652afcc23693b300da306909293ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"104\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5206\u6570\u306e\u5206\u6bcd\u306f\u65b9\u7a0b\u5f0f\u306e\u53f3\u5074\u5168\u4f53\u3092\u9664\u7b97\u3059\u308b\u306e\u3067\u3001\u3082\u3046\u4e00\u65b9\u306e\u5074\u3067\u4e57\u7b97\u3059\u308b\u3053\u3068\u3067\u305d\u308c\u3092\u6e21\u3059\u3053\u3068\u304c\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-f94a174ae36525a6e6ef055e53bb154a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert =\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"172\" 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-e4cffd0cb6eef3c14b8924706cca4a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\vv{n}_1 \\cdot \\vv{n}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u30012 \u3064\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u9593\u306e\u5185\u7a4d\u3092\u6c42\u3081\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-3818384c903fe4f03fd785f0fbfb0197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(1,2,-3) \\cdot (-2,5,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"185\" 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-a0317a3a3ce7f7a3b19d199026305b93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =1 \\cdot (-2) + 2\\cdot 5 +(-3)\\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"223\" 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-c9a5497303548b34fd3bba83bdc588b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =-2 +10-3k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"134\" style=\"vertical-align: -2px;\"><\/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-3f68c05212b2541bc6d1142287eebc18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =8-3k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u672a\u77e5\u306e\u90e8\u5206\u3092\u660e\u3089\u304b\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-5c13e299367327b12f0f781a10c47f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 3k=8\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/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-b126ac6d6422d2ae3c536589c2461e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =}\\mathbf{\\cfrac{8}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" 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\u3001\u7a7a\u9593\u5185\u306e 2 \u3064\u306e\u5e73\u9762\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 (\u516c\u5f0f) \u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u984c\u3092\u898b\u3066\u3001\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306e\u516c\u5f0f \uff12\u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6\u306f\u3001\u524d\u8a18\u5e73\u9762 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%bc%8f-r3-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b-2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%a7%92%e5%ba%a6\/\"> <span class=\"screen-reader-text\">\u7a7a\u9593\u5185\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u89d2\u5ea6 (\u5f0f)<\/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":[15],"tags":[],"class_list":["post-250","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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