{"id":257,"date":"2023-07-10T08:10:10","date_gmt":"2023-07-10T08:10:10","guid":{"rendered":"https:\/\/mathority.org\/ja\/2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%b7%9d%e9%9b%a2%e3%81%ae%e5%85%ac%e5%bc%8f\/"},"modified":"2023-07-10T08:10:10","modified_gmt":"2023-07-10T08:10:10","slug":"2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%b7%9d%e9%9b%a2%e3%81%ae%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%b7%9d%e9%9b%a2%e3%81%ae%e5%85%ac%e5%bc%8f\/","title":{"rendered":"2\u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\uff08\u8a08\u7b97\u5f0f\uff09"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u7279\u306b\u3001\u5b58\u5728\u3059\u308b 2 \u3064\u306e\u65b9\u6cd5\u3068\u3001\u3069\u3061\u3089\u304b\u3092\u4f7f\u7528\u3059\u308b\u65b9\u304c\u3088\u3044\u5834\u5408\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u30012\u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306b\u3064\u3044\u3066\u306f\u4f8b\u984c\u3068\u6f14\u7fd2\u554f\u984c\u304c\u3042\u308a\u3001\u3088\u304f\u7406\u89e3\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-la-distancia-entre-dos-planos\"><\/span> 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7a7a\u9593\u5185\u306e 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306f\u3001\u3053\u308c\u3089 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u76f8\u5bfe\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li> 2 \u3064\u306e\u5e73\u9762\u304c<strong>\u4ea4\u5dee<\/strong>\u307e\u305f\u306f<strong>\u4e00\u81f4\u3059\u308b<\/strong>\u5834\u5408\u3001\u305d\u308c\u3089\u306f\u70b9\u3067\u4ea4\u5dee\u3059\u308b\u305f\u3081\u3001\u305d\u308c\u3089\u306e\u9593\u306e\u8ddd\u96e2\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li> 2 \u3064\u306e\u5e73\u9762\u304c<strong>\u5e73\u884c\u3067<\/strong>\u3042\u308b\u5834\u5408\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306f\u3001\u3044\u305a\u308c\u304b\u306e\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u53d6\u5f97\u3057\u3001\u305d\u306e\u70b9\u3068\u3082\u3046\u4e00\u65b9\u306e\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u5782\u76f4\u9762\u306f\u4ea4\u5dee\u9762\u306e\u4e00\u7a2e\u3067\u3042\u308b\u305f\u3081\u30012 \u3064\u306e\u5782\u76f4\u9762\u9593\u306e\u8ddd\u96e2\u3082\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u305d\u308c\u3089\u306e\u9593\u306e\u76f8\u5bfe\u4f4d\u7f6e\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <a href=\"https:\/\/mathority.org\/ja\/\u7a7a\u9593\u5185\u306e-2-\u3064\u306e\u5e73\u9762\u306e\u76f8\u5bfe\u4f4d\u7f6e-r3-\u306e\u6f14\u7fd2\u554f\u984c\u3092\u89e3\u6c7a\u3057\u305f\u4f8b\/\">2 \u3064\u306e\u5e73\u9762\u306e\u76f8\u5bfe\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3092<\/a>\u77e5\u3063\u3066\u304a\u304f\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u305d\u306e\u65b9\u6cd5\u304c\u3088\u304f\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306f\u3001\u30ea\u30f3\u30af\u3092\u53c2\u7167\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u30ea\u30f3\u30af\u306b\u306f\u3001\u975e\u5e38\u306b\u8a73\u7d30\u306a\u8aac\u660e\u3001\u4f8b\u3001\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-distancia-entre-dos-planos-paralelos\"><\/span> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>2 \u3064\u306e\u5e73\u884c\u306a\u9762\u306f\u5e38\u306b\u540c\u3058\u8ddd\u96e2\u306b\u3042\u308a\u307e\u3059<strong>\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\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>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\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\"> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u3092\u8003\u3048\u307e\u3059\u3002\u4e00\u65b9\u306e\u5e73\u9762\u4e0a\u306e\u70b9\u3068\u3001\u3082\u3046\u4e00\u65b9\u306e\u5e73\u9762\u306e\u4e00\u822c (\u307e\u305f\u306f\u6697\u9ed9\u7684\u306a) \u65b9\u7a0b\u5f0f\u304c\u4e0e\u3048\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-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\">\u4e00\u65b9\u306e\u5e73\u9762\u306e\u70b9\u3092\u901a\u904e\u3059\u308b<strong>2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u516c\u5f0f<\/strong>\u3068\u3001\u3082\u3046\u4e00\u65b9\u306e\u5e73\u9762\u306e\u4e00\u822c\u65b9\u7a0b\u5f0f\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-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>\u3053\u308c\u306f\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u516c\u5f0f\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u5225\u306e\u3055\u3089\u306b\u5358\u7d14\u306a\u65b9\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p> 2 \u3064\u306e\u8a08\u753b\u306e\u9670\u7684 (\u307e\u305f\u306f\u4e00\u822c) \u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 A\u3001B\u3001C \u306f\u6bd4\u4f8b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u554f\u984c\u306e\u4e2d\u3067\u3001\u4fc2\u6570 A\u3001B\u3001C \u304c\u307e\u3063\u305f\u304f\u540c\u3058\u3067\u3042\u308b 2 \u3064\u306e\u5e73\u9762\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u5e73\u9762\u306e\u70b9\u3092\u77e5\u308b\u5fc5\u8981\u304c\u306a\u304f\u3001\u5225\u306e\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\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\"><strong>\u540c\u4e00\u306e\u4fc2\u6570 A\u3001B\u3001C<\/strong>\u3092\u6301\u3064 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u306e\u4e00\u822c (\u307e\u305f\u306f\u9670\u7684) \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 style=\"text-align:left\"> <strong>2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092 2 \u3064\u306e\u5e73\u9762\u306e\u4e00\u822c\u65b9\u7a0b\u5f0f\u304b\u3089\u6c42\u3081\u308b\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-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<\/div>\n<p>\u6700\u7d42\u7684\u306b\u30012 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306f 2 \u3064\u3042\u308a\u307e\u3059\u3002 1 \u3064\u76ee\u306f\u30012 \u3064\u306e\u5e73\u9762\u306e\u3044\u305a\u308c\u304b\u4e0a\u306e\u70b9\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u4fbf\u5229\u3067\u3059\u3002\u305f\u3060\u3057\u30012 \u3064\u306e\u5e73\u9762\u306e\u4e00\u822c\u65b9\u7a0b\u5f0f\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306f\u30012 \u756a\u76ee\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u65b9\u304c\u9069\u5207\u3067\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-distancia-entre-dos-planos-paralelos\"><\/span> 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306e\u8a08\u7b97\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\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\u306b\u95a2\u3059\u308b\u6b21\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<a href=\"https:\/\/mathority.org\/ja\/\u5e73\u9762\u30b7\u3099\u30aa\u30e1\u30c8\u30ea\/\">\u4e00\u65b9\u306e\u5e73\u9762<\/a>\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-entre-dos-planos\"><\/span> 2 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/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\u76f4\u63a5\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 2<\/h3>\n<p>\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-b2bbc524fea8b844e21f44241034b21c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-2y+6z+4=0 \\qquad \\qquad  \\pi_2 : \\ 6x-4y+3z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"471\" 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\u305d\u308c\u3089\u3092\u9694\u3066\u308b\u8ddd\u96e2\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u305d\u308c\u3089\u304c 2 \u3064\u306e\u5e73\u884c\u306a\u5e73\u9762\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u30012 \u3064\u306e\u8a08\u753b\u306e\u4fc2\u6570\u9593\u306e\u6bd4\u4f8b\u95a2\u4fc2\u3092\u78ba\u8a8d\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-3abd37199c65d756bb9c892bf56f0f2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3}{6}=\\cfrac{-2}{-4}\\neq\\cfrac{6}{3} \\neq \\cfrac{4}{1} \\quad \\longrightarrow \\quad \\pi_1 \\ \\cancel{\\parallel} \\ \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"263\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305f\u3060\u3057\u30012 \u3064\u306e\u5e73\u9762\u306e\u4fc2\u6570 A\u3001B\u3001C \u306f\u6bd4\u4f8b\u305b\u305a\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc A \u3068 B \u306e\u307f\u304c\u6bd4\u4f8b\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u5e73\u9762\u306f\u5e73\u884c\u3067\u306f\u306a\u304f\u4ea4\u5dee\u3057\u3066\u304a\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u3089\u306e\u9593\u306e\u8ddd\u96e2\u306f 0 \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-c2ceb0ff96abef105348fa5660ba4fa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(\\pi_1,\\pi_2)=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" 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>\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\u76f4\u63a5\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\u3053\u308c\u306b\u306f\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>\u306b\u5c5e\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\u30012 \u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u7279\u306b\u3001\u5b58\u5728\u3059\u308b 2 \u3064\u306e\u65b9\u6cd5\u3068\u3001\u3069\u3061\u3089\u304b\u3092\u4f7f\u7528\u3059\u308b\u65b9\u304c\u3088\u3044\u5834\u5408\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u30012\u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\u306b\u3064\u3044\u3066\u306f\u4f8b\u984c\u3068\u6f14\u7fd2\u554f\u984c\u304c\u3042\u308a\u3001\u3088\u304f\u7406\u89e3\u3067\u304d\u307e\u3059\u3002 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/2-%e3%81%a4%e3%81%ae%e5%b9%b3%e9%9d%a2%e9%96%93%e3%81%ae%e8%b7%9d%e9%9b%a2%e3%81%ae%e5%85%ac%e5%bc%8f\/\"> <span class=\"screen-reader-text\">2\u3064\u306e\u5e73\u9762\u9593\u306e\u8ddd\u96e2\uff08\u8a08\u7b97\u5f0f\uff09<\/span> \u3082\u3063\u3068\u8aad\u3080 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