{"id":247,"date":"2023-07-10T13:20:19","date_gmt":"2023-07-10T13:20:19","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%86%85%e3%81%ae%e7%82%b9%e3%81%8b%e3%82%89%e5%b9%b3%e9%9d%a2%e3%81%be%e3%81%a7%e3%81%ae%e8%b7%9d%e9%9b%a2%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a7%a3%e7%ad%94%e4%be%8b%e6%bc%94%e7%bf%92\/"},"modified":"2023-07-10T13:20:19","modified_gmt":"2023-07-10T13:20:19","slug":"%e7%a9%ba%e9%96%93%e5%86%85%e3%81%ae%e7%82%b9%e3%81%8b%e3%82%89%e5%b9%b3%e9%9d%a2%e3%81%be%e3%81%a7%e3%81%ae%e8%b7%9d%e9%9b%a2%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a7%a3%e7%ad%94%e4%be%8b%e6%bc%94%e7%bf%92","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%86%85%e3%81%ae%e7%82%b9%e3%81%8b%e3%82%89%e5%b9%b3%e9%9d%a2%e3%81%be%e3%81%a7%e3%81%ae%e8%b7%9d%e9%9b%a2%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a7%a3%e7%ad%94%e4%be%8b%e6%bc%94%e7%bf%92\/","title":{"rendered":"\u7a7a\u9593\u4e0a\u306e\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\uff08\u5f0f\uff09"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u7a7a\u9593\u5185\u306e\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 (\u516c\u5f0f) \u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u3092\u898b\u3066\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\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=\"%c2%bfcual-es-la-distancia-de-un-punto-a-un-plano\"><\/span>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b? <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-105\"><\/div>\n<\/div>\n<p>\u89e3\u6790\u5e7e\u4f55\u5b66\u3067\u306f\u3001<strong>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306f\u3001\u305d\u306e\u70b9\u3068\u5e73\u9762\u4e0a\u306e\u4ed6\u306e\u70b9\u3068\u306e\u9593\u306e\u6700\u77ed\u8ddd\u96e2\u3067\u3059\u3002<\/strong>\u3053\u306e\u8ddd\u96e2\u306f\u3001\u70b9\u304b\u3089\u5e73\u9762\u306b\u5411\u304b\u3046\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u7dda\u5206\u306e\u9577\u3055\u306b\u5bfe\u5fdc\u3057\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\/distance-dun-point-a-un-plan-de-formule.webp\" alt=\"\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b\" class=\"wp-image-3471\" width=\"431\" height=\"227\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distancia-de-un-punto-a-un-plano\"><\/span>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<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>\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u306e\u6982\u5ff5\u3092\u6b63\u78ba\u306b\u7406\u89e3\u3057\u305f\u3089\u3001\u6b21\u306f\u305d\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\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\">\u70b9\u3068\u5e73\u9762\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u306e) \u65b9\u7a0b\u5f0f\u304c\u4e0e\u3048\u3089\u308c\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-224b2b4bb57594d3fa92e148ada43cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x_0,y_0,z_0) \\qquad \\qquad \\pi: \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"><strong>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306f\u6b21<\/strong>\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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u70b9\u304b\u3089\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u306f\u975e\u5e38\u306b\u9762\u5012\u3067\u9577\u3044\u305f\u3081\u3001\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u884c\u3044\u307e\u305b\u3093\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u5f0f\u3092\u9069\u7528\u3057\u305f\u3068\u304d\u306b\u30bc\u30ed\u306b\u7b49\u3057\u3044\u7d50\u679c\u304c\u5f97\u3089\u308c\u305f\u5834\u5408\u3001\u3053\u308c\u306f\u660e\u3089\u304b\u306b\u3001\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u304c\u30bc\u30ed\u3067\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u70b9\u306f\u305d\u306e\u5e73\u9762\u306e\u4e00\u90e8\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u5f0f\u3092\u9069\u7528\u3059\u308b\u306b\u306f\u3001\u8a08\u753b\u3092\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u7684\u306a) \u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5225\u306e\u7a2e\u985e\u306e\u5e73\u9762\u65b9\u7a0b\u5f0f\u3067\u8868\u3059\u5834\u5408\u306f\u3001\u307e\u305a\u4e00\u822c\u65b9\u7a0b\u5f0f\u306b\u5909\u63db\u3057\u3066\u304b\u3089\u305d\u306e\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-de-un-punto-a-un-plano\"><\/span>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u8a08\u7b97\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-109\"><\/div>\n<\/div>\n<p>\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u304c\u6570\u5024\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u6c7a\u5b9a\u3055\u308c\u308b\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u4ee5\u4e0b\u306e\u4f8b\u3092\u89e3\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u70b9 P \u3068\u5e73\u9762 \u03c0 \u306e\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u8981\u70b9\u3068\u8a08\u753b\u3092\u8ff0\u3079\u305f\u4e0a\u3067\u3001\u6b21\u306e\u3088\u3046\u306b\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-19db41565c49be8ca3580630de59813b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,3,-2) \\qquad \\qquad \\pi: \\ 2x+5y-4z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u4e0a\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u793a\u3057\u305f\u5f0f\u3092\u9069\u7528\u3059\u308b\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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/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-6c50799e6cbc0fb28d311858f4c94a82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2\\cdot 1+5\\cdot 3-4\\cdot (-2)+7\\rvert}{\\sqrt{2^2+5^2+(-4)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"282\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\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-805821ed65a28cb8c08ee24473e8bd7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2+15+8+7\\rvert}{\\sqrt{4+25+16}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"199\" style=\"vertical-align: -16px;\"><\/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-ef28713d2c68c0bbb7a25bfd50466811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{32}}{\\bm{\\sqrt{45}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"107\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u5206\u5b50\u306b\u306f\u7d76\u5bfe\u5024\u304c\u3042\u308a\u3001\u5206\u6bcd\u306b\u306f\u5e73\u65b9\u6839\u304c\u3042\u308b\u305f\u3081\u3001\u7d50\u679c\u306f\u5e38\u306b\u6b63\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u8ddd\u96e2\u306f\u8ca0\u306b\u306f\u306a\u3089\u305a\u3001\u5e38\u306b\u6b63\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u7406\u306b\u304b\u306a\u3063\u3066\u3044\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-distancia-entre-dos-planos-paralelos\"><\/span> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u307e\u3059<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u306f\u5e38\u306b\u540c\u3058\u8ddd\u96e2\u96e2\u308c\u3066\u3044\u308b\u305f\u3081\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u30012 \u3064\u306e\u5e73\u9762\u306e\u4e00\u65b9\u306e\u70b9\u3092\u53d6\u5f97\u3057\u3001\u305d\u306e\u70b9\u304b\u3089\u3082\u3046\u4e00\u65b9\u306e\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/strong> <\/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\/distance-entre-deux-plans-paralleles.webp\" alt=\"2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\" class=\"wp-image-2647\" width=\"401\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> 2\u3064\u306e\u5e73\u884c\u306a\u9762\u306e\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3067\u3059\u3002\u305f\u3060\u3057\u30012 \u3064\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 A\u3001B\u3001C \u304c\u4e00\u81f4\u3059\u308b\u5834\u5408\u3001\u3053\u308c\u3092\u884c\u3046\u3055\u3089\u306b\u7c21\u5358\u306a\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u7684\u306a) \u65b9\u7a0b\u5f0f\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-a277aae741d0cfe8200b7c338f57343f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D_1=0 \\qquad \\qquad  \\pi_2 : \\ Ax+By+Cz+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"528\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> <strong>2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21<\/strong>\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-fba7a69f403ec1b933994e987e1ff71b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}} \\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"343\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u3092\u898b\u3064\u3051\u308b\u306e\u306f\u78ba\u304b\u306b\u7c21\u5358\u3067\u3059\u3002\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u6e08\u3080\u305f\u3081\u3067\u3059\u304c\u3001\u305d\u308c\u306f\u554f\u984c\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u4e21\u65b9\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u3001\u597d\u307f\u306e\u65b9\u6cd5\u3092\u9078\u629e\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u304c\u6700\u5584\u3067\u3042\u308b\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306e\u8a08\u7b97\u4f8b<\/h3>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u6b21\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\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-a9cd1abd1a84a5a230fb855c75c59e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 4x-2y-4z+7=0 \\qquad \\qquad  \\pi_2 : \\ 8x-4y-8z+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"471\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u307e\u305a\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u3092\u6271\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762\u65b9\u7a0b\u5f0f\u306e\u3059\u3079\u3066\u306e\u4fc2\u6570\u306f\u72ec\u7acb\u9805\u3092\u9664\u3044\u3066\u6bd4\u4f8b\u3059\u308b\u305f\u3081\u3001\u4e8b\u5b9f\u4e0a 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\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-e13f3d3e18910312a6604d299010da6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{8}=\\cfrac{-2}{-4}=\\cfrac{-4}{-8}\\neq \\cfrac{7}{2} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u30012 \u3064\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u9805 A\u3001B\u3001C \u306f\u4e00\u81f4\u3057\u307e\u305b\u3093\u304c\u30012 \u756a\u76ee\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u5168\u4f53\u3092 2 \u3067\u5272\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3053\u308c\u3092\u5b9f\u73fe\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-d159a803fe606b074b2fbafbf792829d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ \\cfrac{8x-4y-8z+2}{2}=\\cfrac{0}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"204\" style=\"vertical-align: -12px;\"><\/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-0098cb52d72e1305e5cc6daee535dee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 4x-2y-4z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306b\u306f\u3059\u3067\u306b\u540c\u3058\u4fc2\u6570 A\u3001B\u3001C \u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u7c21\u5358\u306b\u8a08\u7b97\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-3f78d3a0f1fd3a6c00acfd51c160dc8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"202\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5024\u3092\u4ee3\u5165\u3057\u3066\u6f14\u7b97\u3092\u89e3\u6c7a\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-ebaa9342424e4e1c6df12cac1f2658fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 1-7\\rvert}{\\sqrt{4^2+(-2)^2+(-4)^2}}= \\cfrac{\\lvert -6\\rvert}{\\sqrt{36}} = \\cfrac{6}{6} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"369\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u3064\u307e\u308a\u3001\u4e00\u65b9\u306e\u5e73\u9762\u3068\u3082\u3046\u4e00\u65b9\u306e\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u306f 1 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-distancia-de-un-punto-a-un-plano\"><\/span>\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u554f\u984c\u3092\u89e3\u304f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u70b9 P \u3068\u3001\u30c7\u30ab\u30eb\u30c8 (\u307e\u305f\u306f\u4e00\u822c) \u65b9\u7a0b\u5f0f\u304c\u6b21\u306e\u3088\u3046\u306a\u5e73\u9762\u3068\u306e\u9593\u306e\u8ddd\u96e2\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-80f2f62e8bfd05d8d6f6d8341c0bb0fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,0,-1) \\qquad \\qquad \\pi: \\ x-3y+2z-4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"339\" 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\">\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u5f0f\u3092\u4f7f\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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5404\u30d1\u30e9\u30e1\u30fc\u30bf\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-23e86b0b23677612b604cb66fb8d63ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 1\\cdot 2+(-3)\\cdot 0+2\\cdot (-1)-4\\rvert}{\\sqrt{1^2+(-3)^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"310\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\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-e947d902a760182e4518c89dd743d9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2+0-2-4\\rvert}{\\sqrt{1+9+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"190\" style=\"vertical-align: -16px;\"><\/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-9f67bf3231fbdd1e0e0be07f3252dace_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -4\\rvert}{\\sqrt{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"112\" style=\"vertical-align: -16px;\"><\/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-0c92e0662fecd16f52c300603444e4dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{4}}{\\bm{\\sqrt{14}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"107\" style=\"vertical-align: -16px;\"><\/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>\u70b9 P \u3068\u5e73\u9762 \u03c0 \u306e\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\uff1a <\/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-4a3458d356f7bffc69bc0f986b1682d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,4,3) \\qquad \\qquad \\pi: \\ y=5x-2z\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" 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\">\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u524d\u306b\u3001\u307e\u305a\u5e73\u9762\u3092\u9670\u7684\u306a (\u307e\u305f\u306f\u4e00\u822c\u7684\u306a) \u65b9\u7a0b\u5f0f\u306e\u5f62\u5f0f\u3067\u8868\u73fe\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-ef28b8fe3e435d42ebba26a0644e4b5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi: \\ -5x+y+2z=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"167\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u3067\u3001\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u3092\u6c7a\u5b9a\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5404\u9805\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-4b60e5f2a3865e5077f484a741ccfe2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -5\\cdot (-1)+1\\cdot 4+2\\cdot 3+0\\rvert}{\\sqrt{(-5)^2+1^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"296\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\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-350cfedc4d96fd5cdd987bd3c9fbcc8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 5+4+6\\rvert}{\\sqrt{25+1+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"173\" style=\"vertical-align: -16px;\"><\/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-ffd92b77650ccab388d90bf6dbd365ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{15}}{\\bm{\\sqrt{30}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"107\" style=\"vertical-align: -16px;\"><\/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>\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u70b9 P \u304c\u5e73\u9762 \u03c0 \u5185\u306b\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\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-0f1172694919a2ec59e99d94477e10e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-3,5) \\qquad \\qquad \\pi: \\ 4x+6y+2z+8=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" 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\">\u70b9\u304c\u5e73\u9762\u306b\u5c5e\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u306b\u306f\u30012 \u3064\u306e\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u8ddd\u96e2\u304c 0 \u306e\u5834\u5408\u3001\u3053\u308c\u306f\u70b9\u304c\u5e73\u9762\u306b\u5c5e\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u4e00\u65b9\u3001\u8ddd\u96e2\u304c 0 \u4ee5\u5916\u306e\u5834\u5408\u3001\u3053\u308c\u306f\u3001\u70b9\u304c\u5e73\u9762\u306b\u5c5e\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u70b9\u306f\u5e73\u9762\u306e\u5916\u5074\u306b\u3042\u308a\u307e\u3059\u3002\u30d7\u30e9\u30f3\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u5f0f\u304b\u3089\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/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-62c5bc20a51cc65d03c68c20f08afc11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 4\\cdot 0+6\\cdot (-3)+2\\cdot 5+8\\rvert}{\\sqrt{4^2+6^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"282\" style=\"vertical-align: -16px;\"><\/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-dc797a0472cb98c5901fc294efe5988c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -18+10+8\\rvert}{\\sqrt{16+36+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"191\" style=\"vertical-align: -16px;\"><\/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-7abeba148ae6b786dcdd35df00f7c308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{0}{\\sqrt{56}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"112\" style=\"vertical-align: -16px;\"><\/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-36660ee3653f3f3fcd120a6016e5dd8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u306f\u30bc\u30ed\u306b\u7b49\u3057\u3044\u305f\u3081\u3001\u4e8b\u5b9f\u4e0a<strong>\u3001\u70b9\u306f\u5e73\u9762\u306b\u5c5e\u3057\u307e\u3059\u3002<\/strong><\/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 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\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-b51c64f5f5d25771ee1eb45d8e37e2f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 2x-y+5z-3=0 \\qquad \\qquad  \\pi_2 : \\ 2x-y+5z-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"453\" 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\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u3092\u6271\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 2 \u3064\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u306f\u3001\u72ec\u7acb\u9805\u3092\u9664\u3044\u3066\u3059\u3079\u3066\u6bd4\u4f8b\u3059\u308b\u305f\u3081\u3001\u3053\u308c\u3089\u306f\u5b9f\u969b\u306b 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\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-4c520445614ecabfaf8a1bda841afa65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{2}=\\cfrac{-1}{-1}=\\cfrac{5}{5} \\neq \\cfrac{-3}{-7} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u5834\u5408\u3001\u4fc2\u6570 A\u3001B\u3001C \u304c\u7b49\u3057\u3044\u305f\u3081\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u6b21\u306e\u5f0f\u3067\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-3f78d3a0f1fd3a6c00acfd51c160dc8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"202\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u5024\u3092\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u6f14\u7b97\u3092\u5b9f\u884c\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-c107ce392f40f085eadf58283ea31fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -7-3\\rvert}{\\sqrt{2^2+(-1)^2+5^2}}= \\cfrac{\\lvert -10\\rvert}{\\sqrt{30}} = \\cfrac{\\bm{10}}{\\bm{\\sqrt{30}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"343\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 5<\/h3>\n<p>\u6b21\u306e 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\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-6d14719b0eefd313552d5257c249c66f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ \\begin{cases} x=3+4\\lambda-2 \\mu \\\\[1.7ex]y=-2+\\lambda+6 \\mu \\\\[1.7ex]z=5-\\lambda+3 \\mu \\end{cases}\\qquad \\qquad  \\pi_2 : \\ 3x+2y-2z-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"477\" style=\"vertical-align: 0px;\"><\/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\">\u524d\u666f\u5e73\u9762\u306f\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u65b9\u7a0b\u5f0f\u306e\u5f62\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u305f\u3081\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u305d\u308c\u3092\u4e00\u822c\u65b9\u7a0b\u5f0f\u306e\u5f62\u5f0f\u306b\u5909\u63db\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u591a\u304f\u306e\u8a08\u7b97\u3068\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u306e\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u53d6\u5f97\u3057\u3001\u305d\u306e\u70b9\u304b\u3089\u4ed6\u306e\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u65b9\u304c\u9ad8\u901f\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762 \u03c0 <sub>1<\/sub>\u304c\u901a\u904e\u3059\u308b\u70b9\u306e\u5ea7\u6a19\u306f\u3001\u5404\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u65b9\u7a0b\u5f0f\u306e\u72ec\u7acb\u9805\u306b\u5bfe\u5fdc\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-d66243e674f3ead58ca1ff6b29a9a715_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u3053\u3067\u3001\u6b21\u306e\u5f0f\u3092\u9069\u7528\u3057\u3066\u3001\u3053\u306e\u70b9\u3068\u4ed6\u306e\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\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-8e667bbf8e826d021b1cb466a3b312ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"307\" style=\"vertical-align: -16px;\"><\/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-e4c4801629feef3733a4564df35d3c46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert 3\\cdot 3+2\\cdot (-2)+(-2)\\cdot 5-9\\rvert}{\\sqrt{3^2+2^2+(-2)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"317\" style=\"vertical-align: -20px;\"><\/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-617538033c94b7606ec4aff058302fd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert 9-4-10-9\\rvert}{\\sqrt{9+4+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"206\" style=\"vertical-align: -16px;\"><\/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-112e5dabc19834e9cd886f6c9296452a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert -14\\rvert}{\\sqrt{17}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"128\" style=\"vertical-align: -16px;\"><\/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-18ff6ac34eed85be881c346ecb7e41dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{14}{\\sqrt{17}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"119\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\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-ef887cbd7e8b9c8bbe88736ce26776d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(\\pi_1,\\pi_2)=d(P,\\pi_2) =} \\cfrac{\\bm{14}}{\\bm{\\sqrt{17}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"204\" style=\"vertical-align: -16px;\"><\/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\u70b9\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 (\u516c\u5f0f) \u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u3092\u898b\u3066\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b? \u89e3\u6790\u5e7e\u4f55\u5b66\u3067\u306f\u3001\u70b9\u304b\u3089\u5e73\u9762\u307e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e7%a9%ba%e9%96%93%e5%86%85%e3%81%ae%e7%82%b9%e3%81%8b%e3%82%89%e5%b9%b3%e9%9d%a2%e3%81%be%e3%81%a7%e3%81%ae%e8%b7%9d%e9%9b%a2%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a7%a3%e7%ad%94%e4%be%8b%e6%bc%94%e7%bf%92\/\"> <span class=\"screen-reader-text\">\u7a7a\u9593\u4e0a\u306e\u70b9\u304b\u3089\u5e73\u9762\u307e\u3067\u306e\u8ddd\u96e2\uff08\u5f0f\uff09<\/span> \u3082\u3063\u3068\u8aad\u3080 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