{"id":11883,"date":"2022-12-26T17:47:51","date_gmt":"2022-12-26T08:47:51","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11883"},"modified":"2023-01-01T05:44:01","modified_gmt":"2022-12-31T20:44:01","slug":"vector-12","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-12.html","title":{"rendered":"\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\uff1a\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f"},"content":{"rendered":"\n<p>\u79c1\u305f\u3061\u306f\u7dda\u3084\u9762\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u6570\u5b66\u3067\u5b66\u3073\u307e\u3059\u3002\u305f\u3060\u3001\u3053\u308c\u3089\u306f\u5e73\u9762\u3067\u306e\u8a08\u7b97\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u5ea7\u6a19\u3067\u7dda\u3084\u9762\u306e\u8a08\u7b97\u3092\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u7acb\u4f53\u56f3\u5f62\u306e\u8a08\u7b97\u3067\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7acb\u4f53\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u5e73\u9762\u3084\u7a7a\u9593\u306e\u76f4\u7dda\u3092\u8868\u73fe\u3067\u304d\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u3089\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u7403\u9762\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u3092\u8a08\u7b97\u3057\u305f\u308a\u3001\u5e73\u9762\u3068\u76f4\u7dda\u306b\u3088\u308b\u306a\u3059\u89d2\u3092\u5f97\u305f\u308a\u3059\u308b\u306e\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u8a08\u7b97\u306b\u306f\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306e\u4e21\u65b9\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u4f7f\u3044\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u516c\u5f0f<\/h2>\n<p>\u307e\u305a\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\\(ax+by+c=0\\)\u306b\u3088\u308a\u3001\u4e8c\u6b21\u5143\u3067\u306e\u76f4\u7dda\u3092\u8868\u305b\u308b\u3053\u3068\u306f\u3059\u3067\u306b\u77e5\u3063\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u305f\u3060\u7a7a\u9593\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306f\u4e8c\u6b21\u5143\u3067\u306f\u306a\u304f\u4e09\u6b21\u5143\u3067\u3042\u308b\u305f\u3081\u3001\\(z\\)\u8ef8\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u7a7a\u9593\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(ax+by+cz+d=0\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn1.jpg\" alt=\"\" width=\"534\" height=\"283\" class=\"aligncenter size-full wp-image-11897\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u4e8c\u6b21\u5143\u3067\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3057\u3066\u3001\\(z\\)\u8ef8\u306e\u8981\u7d20\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u5ea7\u6a19\u3067\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3068\u304d\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u304c\u4fbf\u5229\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u307e\u305a\u306f\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u4e09\u6b21\u5143\u7a7a\u9593\u306b\u5b58\u5728\u3059\u308b\u5e73\u9762\u306b\u3064\u3044\u3066\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{n}\\)\u3092\u7528\u3044\u3066\u8868\u305b\u307e\u3059\u3002<\/span>\u7279\u5b9a\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u3001\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u304c\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u306a\u305c\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u304b\u3068\u3044\u3046\u3068\u3001\u5e73\u9762\u3067\u306f\u7279\u5b9a\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u3059\u3079\u3066\u306e\u4f4d\u7f6e\u3067\u5782\u76f4\u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn2.jpg\" alt=\"\" width=\"284\" height=\"264\" class=\"aligncenter size-full wp-image-11898\" \/><\/p>\n<p>\u305d\u3053\u3067\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3059\u308b\u70b9A\u3068\u70b9P\u306b\u5bfe\u3057\u3066\u3001\u5782\u76f4\u306a\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{n}\\)\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u70b9A\u3068\u70b9P\u304c\u5e73\u9762\u4e0a\u306e\u3069\u3053\u306b\u5b58\u5728\u3057\u3066\u3044\u305f\u3068\u3057\u3066\u3082\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{n}\\)\u306b\u5782\u76f4\u306a\u306e\u3067\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{AP}\u00b7\\overrightarrow{n}=0\\)<\/p>\n<p>\\((\\overrightarrow{p}-\\overrightarrow{a})\u00b7\\overrightarrow{n}=0\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn3.jpg\" alt=\"\" width=\"228\" height=\"183\" class=\"aligncenter size-full wp-image-11899\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u5b9a\u70b9A\u3092\\(\\overrightarrow{a}=(x_1,y_1,z_1)\\)\u3001\u5e73\u9762\u4e0a\u306e\u4efb\u610f\u306e\u70b9P\u3092\\(\\overrightarrow{p}=(x,y,z)\\)\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\\(\\overrightarrow{n}=(a,b,c)\\)\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5148\u307b\u3069\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3088\u308a\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\((x-x_1)a+(y-y_1)b+(z-z_1)c\\)\\(=0\\)<\/p>\n<p>\\(ax+by+cz-(ax_1+by_1+cz_1)\\)\\(=0\\)<\/p>\n<p>A\u306f\u5b9a\u70b9\u3067\u3042\u308b\u305f\u3081\u3001\u5ea7\u6a19\u306f\u660e\u78ba\u306b\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3082\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(ax_1+by_1+cz_1\\)\u306f\u5b9a\u6570\u3067\u3059\u3002\u305d\u3053\u3067\\(ax_1+by_1+cz_1=-d\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5148\u307b\u3069\u8a18\u3057\u305f\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(ax+by+cz+d=0\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u3001A\\((1,1,-1)\\)\u3001B\\((0,2,3)\\)\u3001C\\((-1,0,4)\\)\u3092\u901a\u308b\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(ax+by+cz+d=0\\)\u3078\u4ee3\u5165\u3057\u3001\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a+b-c+d=0\\) &#8211; \u2460<\/li>\n<li>\\(2b+3c+d=0\\) &#8211; \u2461<\/li>\n<li>\\(-a+4c+d=0\\) &#8211; \u2462<\/li>\n<\/ul>\n<p><strong>\u30fb\\(\u2460-\u2461\\)\u3088\u308a<\/strong><\/p>\n<p>\\(a-b-4c=0\\) &#8211; \u2463<\/p>\n<p><strong>\u30fb\\(\u2461-\u2462\\)\u3088\u308a<\/strong><\/p>\n<p>\\(a+2b-c=0\\) &#8211; \u2464<\/p>\n<p><strong>\u30fb\\(\u2463-\u2464\u00d74\\)\u3088\u308a<\/strong><\/p>\n<p>\\(-3a-9b=0\\)<\/p>\n<p>\\(b=-\\displaystyle\\frac{1}{3}a\\)<\/p>\n<p><strong>\u30fb\\(\u2463\u00d72+\u2464\\)\u3088\u308a<\/strong><\/p>\n<p>\\(3a-9c=0\\)<\/p>\n<p>\\(c=\\displaystyle\\frac{1}{3}a\\)<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u2460\u3078\\(b=-\\displaystyle\\frac{1}{3}a\\)\u3068\\(c=\\displaystyle\\frac{1}{3}a\\)\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a+b-c+d=0\\)<\/p>\n<p>\\(a-\\displaystyle\\frac{1}{3}a-\\displaystyle\\frac{1}{3}a+d=0\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{3}a+d=0\\)<\/p>\n<p>\\(d=-\\displaystyle\\frac{1}{3}a\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3078\\(b=-\\displaystyle\\frac{1}{3}a\\)\u3001\\(c=\\displaystyle\\frac{1}{3}a\\)\u3001\\(d=-\\displaystyle\\frac{1}{3}a\\)\u3092\u4ee3\u5165\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(ax-\\displaystyle\\frac{1}{3}ay+\\displaystyle\\frac{1}{3}az-\\displaystyle\\frac{1}{3}a\\)\\(=0\\)<\/p>\n<p>\\(3ax-ay+az-a=0\\)<\/p>\n<p>\\(a\u22600\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4e21\u8fba\u3092\\(a\\)\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(3x-y+z-1=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u306a\u304a\u7a7a\u9593\u5ea7\u6a19\u306e\u5e73\u9762\u3092\u6c7a\u3081\u308b\u3068\u304d\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u306a\u3044\u65b9\u6cd5\u3082\u3042\u308a\u307e\u3059\u30022\u3064\u306e\u70b9\uff08\u70b9A\u3068\u70b9B\uff09\u3092\u901a\u308b\u7a7a\u9593\u306e\u5e73\u9762\u3067\u306f\u3001\u7279\u5b9a\u306e\u5e73\u9762\u3092\u6307\u5b9a\u3067\u304d\u307e\u305b\u3093\u3002\u8fbaAB\u3092\u8ef8\u306b\u56de\u8ee2\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn4.jpg\" alt=\"\" width=\"403\" height=\"281\" class=\"aligncenter size-full wp-image-11901\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u306a\u3044\u5834\u5408\u3001AB\u306b\u52a0\u3048\u3066\u70b9C\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<span style=\"color: #0000ff;\">\u7acb\u4f53\u3067\u306f\u30013\u3064\u306e\u70b9\u3092\u901a\u308b\u5834\u5408\u3001\u4e00\u3064\u306e\u5e73\u9762\u3092\u7279\u5b9a\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p>\u307e\u305f\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u300c\u5171\u9762\u6761\u4ef6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001A\u3001B\u3001C\u306e3\u70b9\u3092\u901a\u308b\u5e73\u9762\u4e0a\u306e\u70b9P\u3092\u8868\u305b\u308b\u300d\u3053\u3068\u3092\u3059\u3067\u306b\u5b66\u3093\u3067\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001<span style=\"color: #ff0000;\">\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5171\u9762\u6761\u4ef6\u3068\u3044\u3046\u306e\u306f\u3001\u7acb\u4f53\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u3082\u3042\u308b\u306e\u3067\u3059\u3002<\/span><\/p>\n<p>\u305d\u3053\u3067\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3001\u70b9B\uff08\\(\\overrightarrow{b}\\)\uff09\u3001\u70b9C\uff08\\(\\overrightarrow{c}\\)\uff09\u3092\u901a\u308b\u5e73\u9762\u306b\u3064\u3044\u3066\u3001\u5e73\u9762\u4e0a\u306b\u3042\u308b\u4efb\u610f\u306e\u70b9\u3092P\uff08\\(\\overrightarrow{p}\\)\uff09\u3068\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=s\\overrightarrow{a}+t\\overrightarrow{b}+u\\overrightarrow{c}\\)<\/li>\n<li>\\(s+t+u=1\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dkdh7.jpg\" alt=\"\" width=\"600\" height=\"224\" class=\"aligncenter size-full wp-image-11854\" \/><\/p>\n<p>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5171\u9762\u6761\u4ef6\u3068\u7acb\u4f53\u5ea7\u6a19\u3067\u306e\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u3092\u5b66\u3079\u3070\u3001\u30d9\u30af\u30c8\u30eb\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u3088\u308a\u7406\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h2>\n<p>\u6b21\u306b\u3001\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<span style=\"color: #0000ff;\">\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306e\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u516c\u5f0f\u304c\u540c\u3058\u3067\u3059\u3002<\/span>\u5b9a\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3092\u901a\u308a\u3001\u7279\u5b9a\u306e\u65b9\u5411\u3092\u3082\u3064\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{d}\\)\u306b\u5e73\u884c\u306a\u70b9P\uff08\\(\\overrightarrow{p}\\)\uff09\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{d}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb2.jpg\" alt=\"\" width=\"325\" height=\"171\" class=\"aligncenter size-full wp-image-11738\" \/><\/p>\n<p>\\(t\\)\u306f\u5b9f\u6570\u3067\u3042\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u5024\u306b\u306a\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u70b9P\u304c\u3064\u306a\u304c\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u76f4\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb3.jpg\" alt=\"\" width=\"600\" height=\"219\" class=\"aligncenter size-full wp-image-11739\" \/><\/p>\n<p>\u307e\u305f\u7570\u306a\u308b2\u70b9\uff08A\u3068B\uff09\u3092\u901a\u308b\u7a7a\u9593\u306e\u76f4\u7dda\u306b\u3064\u3044\u3066\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=(1-t)\\overrightarrow{a}+t\\overrightarrow{b}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb13.jpg\" alt=\"\" width=\"538\" height=\"209\" class=\"aligncenter size-full wp-image-11750\" \/><\/p>\n<p>2\u70b9\u3092\u901a\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570\u3092\u8db3\u3059\u3068\u5fc5\u305a1\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u3082\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3068\u540c\u3058\u3067\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3082\u3001\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002<\/p>\n<h3>\u4e00\u3064\u306e\u70b9\u3092\u901a\u308b\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5148\u307b\u3069\u306e\u77e5\u8b58\u3092\u5229\u7528\u3057\u3066\u7acb\u4f53\u5ea7\u6a19\u3067\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3057\u307e\u3057\u3087\u3046\u3002\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u306f\u516c\u5f0f\u304c\u540c\u3058\u3067\u3042\u308b\u3082\u306e\u306e\u3001\u7acb\u4f53\u5ea7\u6a19\u3067\u306f\\(z\\)\u8ef8\u304c\u52a0\u308f\u308b\u305f\u3081\u3001\u5e73\u9762\u5ea7\u6a19\u3068\u7acb\u4f53\u5ea7\u6a19\u3067\u306f\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u304c\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u5b9a\u70b9A\u3092\\(\\overrightarrow{a}=(x_1,y_1,z_1)\\)\u3001\u76f4\u7dda\u4e0a\u306e\u4efb\u610f\u306e\u70b9P\u3092\\(\\overrightarrow{p}=(x,y,z)\\)\u3001\\(\\overrightarrow{d}=(l,m,n)\\)\u3068\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{d}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\((x,y,z)=(x_1+tl,y_1+tm,z_1+tn)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(x=x_1+tl\\)\u3001\\(y=y_1+tm\\)\u3001\\(z=z_1+tn\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\\(t\\)\u306e\u5f0f\u306b\u305d\u308d\u3048\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(t=\\displaystyle\\frac{x-x_1}{l}\\)<\/li>\n<li>\\(t=\\displaystyle\\frac{y-y_1}{m}\\)<\/li>\n<li>\\(t=\\displaystyle\\frac{z-z_1}{n}\\)<\/li>\n<\/ul>\n<p>\u540c\u3058\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u5f53\u7136\u306a\u304c\u3089\\(t\\)\u306e\u5024\u304c\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{x-x_1}{l}=\\displaystyle\\frac{y-y_1}{m}=\\displaystyle\\frac{z-z_1}{n}\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u304c\u7a7a\u9593\u3067\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n<h3>\u4e8c\u3064\u306e\u70b9\u3092\u901a\u308b\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u4e00\u65b9\u3001\u4e8c\u3064\u306e\u70b9\u3092\u901a\u308b\u5834\u5408\u3067\u306f\u3001\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u70b9A\u3092\\(\\overrightarrow{a}=(x_1,y_1,z_1)\\)\u3001\u70b9B\u3092\\(\\overrightarrow{a}=(x_2,y_2,z_2)\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d<span style=\"color: #0000ff;\">\u5148\u307b\u3069\u306e\\(\\overrightarrow{d}\\)\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{d}=\\overrightarrow{AB}\\)\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span>\u307e\u305f\u3001\\(\\overrightarrow{AB}=(x_2-x_1,y_2-y_1,z_2-z_1)\\)\u3067\u3059\u3002\\(\\overrightarrow{d}=(l,m,n)\\)\u306a\u306e\u3067\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(l=x_2-x_1\\)<\/li>\n<li>\\(m=y_2-y_1\\)<\/li>\n<li>\\(n=z_2-z_1\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\\(l=x_2-x_1\\)\u3001\\(m=y_2-y_1\\)\u3001\\(n=z_2-z_1\\)\u3092\\(\\displaystyle\\frac{x-x_1}{l}\\)\\(=\\displaystyle\\frac{y-y_1}{m}\\)\\(=\\displaystyle\\frac{z-z_1}{n}\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{x-x_1}{x_2-x_1}=\\displaystyle\\frac{y-y_1}{y_2-y_1}=\\displaystyle\\frac{z-z_1}{z_2-z_1}\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u30012\u70b9\u3092\u901a\u308b\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u76f4\u7dda\u3068\u5e73\u9762\u306e\u306a\u3059\u89d2\uff1a\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5229\u7528<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u5185\u5bb9\u3092\u5229\u7528\u3057\u3066\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u5e73\u9762\\(x-4y+z=0\\)\u3068\u76f4\u7dda\\(\\displaystyle\\frac{x-2}{4}\\)\\(=\\displaystyle\\frac{y+1}{-1}\\)\\(=z-3\\)\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u306a\u3059\u89d2\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u76f4\u7dda\\(\\displaystyle\\frac{x-2}{4}\\)\\(=\\displaystyle\\frac{y+1}{-1}\\)\\(=z-3\\)\u3068\u3044\u3046\u306e\u306f\u3001\u5b9a\u70b9\\((2,-1,3)\\)\u3092\u901a\u308a\u3001\\(\\overrightarrow{d}=(4.-1,1)\\)\u306b\u5e73\u884c\u306a\u76f4\u7dda\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u7a7a\u9593\u5ea7\u6a19\u3067\u5e73\u9762\u3068\u76f4\u7dda\u306e\u89d2\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u5e73\u9762\u306b\u5bfe\u3057\u3066\u3001\u5fc5\u305a\u5782\u76f4\u306b\u306a\u308b\u306e\u304c\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3068\u76f4\u7dda\u306e\u89d2\u5ea6\u304c\u308f\u304b\u308c\u3070\u3001\u5e73\u9762\u3068\u76f4\u7dda\u306e\u89d2\u5ea6\u304c\u308f\u304b\u308b\u306e\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn5.jpg\" alt=\"\" width=\"228\" height=\"212\" class=\"aligncenter size-full wp-image-11906\" \/><\/p>\n<p>\u5e73\u9762\\(ax+by+cz+d=0\\)\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{n}=(a,b,c)\\)\u306f\u5fc5\u305a\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(x-4y+z=0\\)\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f\\(\\overrightarrow{n}=(1,-4,1)\\)\u3067\u3059\u3002\u65b9\u7a0b\u5f0f\u3068\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u95a2\u4fc2\u306f\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\\(\\overrightarrow{d}=(4.-1,1)\\)\u3068\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{n}=(1,-4,1)\\)\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u306a\u3059\u89d2\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u3002\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u89d2\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(|\\overrightarrow{d}|=\\sqrt{4^2+(-1)^2+1^2)}\\)\\(=3\\sqrt{2}\\)<\/li>\n<li>\\(|\\overrightarrow{n}|=\\sqrt{1^2+(-4)^2+1^2)}\\)\\(=3\\sqrt{2}\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\u5185\u7a4d\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{d}\u00b7\\overrightarrow{n}\\)<\/p>\n<p>\\(=4\u00d71+(-1)\u00d7-4+1\u00d71\\)<\/p>\n<p>\\(=9\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u89d2\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{d}\u00b7\\overrightarrow{n}=|\\overrightarrow{d}||\\overrightarrow{n}|cos\u03b8\\)<\/p>\n<p>\\(9=3\\sqrt{2}\u00d73\\sqrt{2}\u00d7cos\u03b8\\)<\/p>\n<p>\\(cos\u03b8=\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\u03b8=60\u00b0\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn6.jpg\" alt=\"\" width=\"216\" height=\"145\" class=\"aligncenter size-full wp-image-11907\" \/><\/p>\n<p>\u305f\u3060\u3001\\(\\overrightarrow{d}\\)\u3068\\(\\overrightarrow{n}\\)\u306e\u306a\u3059\u89d2\u304c60\u00b0\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u76f4\u7dda\u3068\u5e73\u9762\u306e\u306a\u3059\u89d2\u306f\\(90-60=30\u00b0\\)\u3067\u3059\u3002<\/p>\n<h3>\u7403\u9762\u3068\u5e73\u9762\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u5186\u306e\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u3082\u3046\u4e00\u3064\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u7403\u9762\u3068\u5e73\u9762\u304c\u4ea4\u308f\u308b\u3068\u304d\u3001\u4ea4\u70b9\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u306e\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u4e2d\u5fc3C\u304c\\((-1,2,3)\\)\u3067\u3042\u308a\u3001\u534a\u5f84\u304c6\u306e\u7403\u306b\u3064\u3044\u3066\u3001\u5e73\u9762\\(x-2y-4z-4=0\\)\u3068\u306e\u4ea4\u70b9\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u5186\u306e\u4e2d\u5fc3H\u306e\u5ea7\u6a19\u3068\u534a\u5f84\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u4e2d\u5fc3C\u304c\\((-1,2,3)\\)\u3067\u3042\u308a\u3001\u534a\u5f84\u304c6\u306e\u7403\u3067\u3042\u308b\u305f\u3081\u3001\u7403\u9762\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((x+1)^2+(y-2)^2+(z-3)^2=36\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\u7403\u306e\u4e2d\u5fc3\u304b\u3089\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306b\u7dda\u3092\u4e0b\u308d\u3059\u3068\u304d\u3001\u4ea4\u70b9\u3092H\u3068\u3057\u307e\u3059\u3002\u4ea4\u70b9H\u306f\u7403\u9762\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u5186\u306e\u4e2d\u5fc3\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn8.jpg\" alt=\"\" width=\"313\" height=\"179\" class=\"aligncenter size-full wp-image-11909\" \/><\/p>\n<p>\u5e73\u9762\\(x-2y-4z-4=0\\)\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306a\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f\\(\\overrightarrow{n}=(1,-2,-4)\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u7403\u306e\u4e2d\u5fc3\\((-1,2,3)\\)\u3092\u901a\u308a\u3001\\(\\overrightarrow{n}=(1,-2,-4)\\)\u306b\u5e73\u884c\u306a\u76f4\u7dda\uff08\u8fbaCH\uff09\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x+1=\\displaystyle\\frac{y-2}{-2}=\\displaystyle\\frac{z-3}{-4}\\)\\(=t\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(t\\)\u3092\u542b\u3080\u5f0f\u3078\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(x=t-1\\)<\/li>\n<li>\\(y=-2t+2\\)<\/li>\n<li>\\(z=-4t+3\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u3001\u70b9H\u306f\u5e73\u9762\\(x-2y-4z-4=0\\)\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x-2y-4z-4=0\\)<\/p>\n<p>\\((t-1)-2(-2t+2)\\)\\(-4(-4t+3)-4\\)\\(=0\\)<\/p>\n<p>\\(21t-21=0\\)<\/p>\n<p>\\(t=1\\)<\/p>\n<p>\\(t=1\\)\u3067\u3042\u308b\u305f\u3081\u3001\u70b9H\u306e\u5ea7\u6a19\u306f\\((0,0,-1)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u7403\u9762\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u5186\u306e\u4e2d\u5fc3H\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u306a\u304a\u70b9C\u306e\u5ea7\u6a19\u306f\\((-1,2,3)\\)\u3067\u3042\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u3066CH\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(|\\overrightarrow{CH}|\\)\\(=\\sqrt{(0+1)^2+(0-2)^2+(-1-3)^2}\\)<\/p>\n<p>\\(|\\overrightarrow{CH}|=\\sqrt{21}\\)<\/p>\n<p>\u307e\u305f\u7403\u306e\u534a\u5f84\u306f6\u3067\u3042\u308b\u305f\u3081\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u5186\u306e\u534a\u5f84\\(r\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(6^2=r^2+(\\sqrt{21})^2\\)<\/p>\n<p>\\(r^2=15\\)<\/p>\n<p>\\(r=\\sqrt{15}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u5186\u306e\u4e2d\u5fc3\u5ea7\u6a19\u3060\u3051\u3067\u306a\u304f\u3001\u5186\u306e\u534a\u5f84\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u516c\u5f0f\u3092\u899a\u3048\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u5f0f\u3092\u5909\u5f62\u3057\u306a\u3051\u308c\u3070\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u7a7a\u9593\u56f3\u5f62\u3067\u306e\u5e73\u9762\u3068\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b<\/h2>\n<p>\u7a7a\u9593\u5ea7\u6a19\u3067\u91cd\u8981\u306a\u6982\u5ff5\u304c\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3084\u7a7a\u9593\u3067\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\u7a7a\u9593\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u7279\u5b9a\u306e\u70b9\u3092\u901a\u308b\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u5fdc\u7528\u554f\u984c\u3067\u306f\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u3068\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306e\u4e21\u65b9\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u70b9\u306e\u5ea7\u6a19\u3084\u7dda\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u7acb\u4f53\u56f3\u5f62\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u5ea7\u6a19\u3092\u7528\u3044\u308b\u65b9\u7a0b\u5f0f\u306e\u4e21\u65b9\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u79c1\u305f\u3061\u306f\u7dda\u3084\u9762\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u6570\u5b66\u3067\u5b66\u3073\u307e\u3059\u3002\u305f\u3060\u3001\u3053\u308c\u3089\u306f\u5e73\u9762\u3067\u306e\u8a08\u7b97\u3067\u3059\u3002\u305d\u308c\u30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