{"id":11850,"date":"2022-12-25T14:24:04","date_gmt":"2022-12-25T05:24:04","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11850"},"modified":"2022-12-30T07:59:56","modified_gmt":"2022-12-29T22:59:56","slug":"vector-10","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-10.html","title":{"rendered":"\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u56f3\u5f62\uff1a\u516c\u5f0f\u3084\u5e73\u9762\u3068\u306e\u4ea4\u70b9\u5ea7\u6a19"},"content":{"rendered":"\n<p>\u30d9\u30af\u30c8\u30eb\u3067\u91cd\u8981\u306a\u6982\u5ff5\u306b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059\u3002\u539f\u70b9O\u3092\u59cb\u70b9\u3068\u3059\u308b\u30d9\u30af\u30c8\u30eb\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6982\u5ff5\u306f\u540c\u3058\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u5229\u7528\u3059\u308b\u516c\u5f0f\u306f\u540c\u3058\u3067\u3042\u308a\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u306a\u304a\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306b\u7279\u6709\u306e\u6761\u4ef6\u306b\u5171\u9762\u6761\u4ef6\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3053\u306e\u6761\u4ef6\u306b\u3064\u3044\u3066\u3082\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5b66\u3093\u3067\u3044\u308b\u5834\u5408\u306f\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3069\u306e\u3088\u3046\u306b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3001\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u306e\u516c\u5f0f\u3084\u554f\u984c\u306e\u89e3\u304d\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5185\u5206\u70b9\u3001\u5916\u5206\u70b9\u3001\u91cd\u5fc3\u306e\u516c\u5f0f<\/h2>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u3001\\(z\\)\u6210\u5206\u304c\u52a0\u308f\u308b\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3082\u307b\u307c\u540c\u3058\u6982\u5ff5\u3067\u3059\u3002\u4e8b\u5b9f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\u5185\u5206\u70b9\u306e\u516c\u5f0f\u3001\u5916\u5206\u70b9\u306e\u516c\u5f0f\u3001\u91cd\u5fc3\u306e\u516c\u5f0f\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u70b9A\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{a}\\)\u3068\u70b9B\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{b}\\)\u306b\u3064\u3044\u3066\u3001\u7dda\u5206AB\u3092\\(m:n\\)\u306b\u5185\u5206\u3059\u308b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{p}\\)\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\displaystyle\\frac{n\\overrightarrow{a}+m\\overrightarrow{b}}{m+n}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dkdh5.jpg\" alt=\"\" width=\"350\" height=\"268\" class=\"aligncenter size-full wp-image-11852\" \/><\/p>\n<p>\u307e\u305f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5916\u5206\u70b9\u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\displaystyle\\frac{-n\\overrightarrow{a}+m\\overrightarrow{b}}{m-n}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dkdh6.jpg\" alt=\"\" width=\"350\" height=\"267\" class=\"aligncenter size-full wp-image-11853\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5185\u5206\u70b9\u30fb\u5916\u5206\u70b9\u306e\u516c\u5f0f\u3068\u307e\u3063\u305f\u304f\u540c\u3058\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span>\u91cd\u5fc3G\u3092\u5f97\u308b\u516c\u5f0f\u3082\u540c\u3058\u3067\u3042\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(G=\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u304c\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u899a\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u5185\u5bb9\u304c\u307b\u3068\u3093\u3069\u306a\u3044\u7406\u7531\u3067\u3059\u3002<\/p>\n<h3>\u5171\u7dda\u6761\u4ef6\u30fb\u5171\u70b9\u6761\u4ef6\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u540c\u3058<\/h3>\n<p>\u305d\u308c\u3060\u3051\u3067\u306a\u304f\u3001<span style=\"color: #0000ff;\">\u5171\u7dda\u6761\u4ef6\u30fb\u5171\u70b9\u6761\u4ef6\u3082\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u540c\u3058\u3067\u3059\u3002<\/span>\u540c\u3058\u7dda\u4e0a\u306b\u30d9\u30af\u30c8\u30eb\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{AP}=k\\overrightarrow{AB}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odn2.jpg\" alt=\"\" width=\"398\" height=\"135\" class=\"aligncenter size-full wp-image-11699\" \/><\/p>\n<p>\u70b9A\u3001\u70b9B\u3001\u70b9P\u304c\u540c\u3058\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3059\u308b\u306e\u3067\u3042\u308c\u3070\u3001\\(\\overrightarrow{AB}\\)\u3092\u5b9f\u6570\u500d\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\\(\\overrightarrow{AP}\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u5834\u5408\u3001\u540c\u3058\u70b9\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u5171\u70b9\u6761\u4ef6\u3068\u3044\u3044\u307e\u3059\u3002\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u540c\u3058\u70b9\u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3057\u305f\u3044\u5834\u5408\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5171\u9762\u6761\u4ef6\u3067\u306f\u3001\u4fc2\u6570\u3092\u8db3\u3059\u30681\u306b\u306a\u308b<\/h3>\n<p>\u306a\u304a\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u5171\u9762\u6761\u4ef6\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u7dda\u306e\u307f\u3092\u8003\u3048\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u4e00\u65b9\u3067\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u7acb\u4f53\u56f3\u5f62\u3067\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u7279\u5b9a\u306e\u9762\u306b\u5b58\u5728\u3059\u308b\u70b9\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u70b9A\u3068\u70b9B\u3092\u901a\u308b\u76f4\u7dda\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=s\\overrightarrow{a}+t\\overrightarrow{b}\\)<\/li>\n<li>\\(s+t=1\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/efje2.jpg\" alt=\"\" width=\"435\" height=\"217\" class=\"aligncenter size-full wp-image-11762\" \/><\/p>\n<p>\\(s+t=1\\)\u3001\u3064\u307e\u308a\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570\u3092\u8db3\u3057\u30661\u306b\u306a\u308b\u5834\u5408\u30012\u3064\u306e\u70b9\u3092\u901a\u308b\u76f4\u7dda\u3092\u8868\u305b\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u70b9P\uff08\\(\\overrightarrow{p}\\)\uff09\u306f\u8fbaAB\u4e0a\u306e\u3069\u3053\u304b\u306b\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<p>\u300c\u4fc2\u6570\u3092\u8db3\u3057\u30661\u306b\u3059\u308b\u300d\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u91cd\u8981\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u4fc2\u6570\u3092\u8db3\u3057\u30661\u306b\u306a\u308b\u5834\u5408\u3001\u4f55\u3092\u610f\u5473\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\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>\u3053\u308c\u306f\u3001<span style=\"color: #ff0000;\">\u70b9P\u304c\u300c\u70b9A\u3001\u70b9B\u3001\u70b9C\u3092\u901a\u308b\u5e73\u9762\u300d\u306e\u4e0a\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\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>\u3053\u308c\u304c\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5171\u9762\u6761\u4ef6\u3067\u3059\u3002\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u4fc2\u6570\u304c1\u306e\u5834\u5408\u30013\u3064\u306e\u70b9\u3092\u901a\u308b\u9762\u4e0a\u306b\u70b9P\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u70b9\u306e\u4f4d\u7f6e\u3092\u6c7a\u5b9a\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u5185\u5bb9\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7b54\u3048\u3092\u5f97\u308b\u306e\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u56db\u9762\u4f53OBCD\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{OP}+3\\overrightarrow{AP}\\)\\(+2\\overrightarrow{BP}\\)\\(+6\\overrightarrow{CP}\\)\\(=\\overrightarrow{0}\\)\u3092\u6e80\u305f\u3059\u70b9P\u306f\u3069\u306e\u3088\u3046\u306a\u70b9\u3067\u3057\u3087\u3046\u304b\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{OP}+3\\overrightarrow{AP}\\)\\(+2\\overrightarrow{BP}\\)\\(+6\\overrightarrow{CP}\\)\\(=\\overrightarrow{0}\\)<\/p>\n<p>\\(\\overrightarrow{OP}+3(\\overrightarrow{OP}-\\overrightarrow{OA})\\)\\(+2(\\overrightarrow{OP}-\\overrightarrow{OB})\\)\\(+6(\\overrightarrow{OP}-\\overrightarrow{OC})\\)\\(=\\overrightarrow{0}\\)<\/p>\n<p>\\(12\\overrightarrow{OP}-3\\overrightarrow{OA}-2\\overrightarrow{OB}\\)\\(-6\\overrightarrow{OC}\\)\\(=\\overrightarrow{0}\\)<\/p>\n<p>\\(\\overrightarrow{OP}=\\displaystyle\\frac{1}{12}(3\\overrightarrow{OA}+2\\overrightarrow{OB}\\)\\(+6\\overrightarrow{OC})\\)<\/p>\n<p>\u305f\u3060\u3001\u3053\u3053\u307e\u3067\u306e\u8a08\u7b97\u3067\u306f\u70b9P\u304c\u3069\u306e\u3088\u3046\u306a\u70b9\u306a\u306e\u304b\u308f\u304b\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{OP}=\\displaystyle\\frac{1}{12}\\)\\(\\left(5\u00b7\\displaystyle\\frac{3\\overrightarrow{OA}+2\\overrightarrow{OB}}{2+3}+6\\overrightarrow{OC}\\right)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9P\u306f\u7dda\u5206AB\u3092\\(2:3\\)\u306b\u5185\u5206\u3059\u308b\u3053\u3068\u3068\u95a2\u4fc2\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\\(\\displaystyle\\frac{3\\overrightarrow{OA}+2\\overrightarrow{OB}}{2+3}=\\overrightarrow{OD}\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u70b9D\uff08\\(\\overrightarrow{OD}\\)\uff09\u306f\u7dda\u5206AB\u3092\\(2:3\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3067\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{OP}=\\displaystyle\\frac{1}{12}\\)\\((5\\overrightarrow{OD}+6\\overrightarrow{OC})\\)<\/p>\n<p>\\(\\overrightarrow{OP}=\\displaystyle\\frac{11}{12}\\)\\(\\left(\\displaystyle\\frac{5\\overrightarrow{OD}+6\\overrightarrow{OC}}{6+5}\\right)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9P\u306f\u7dda\u5206DC\u3092\\(6:5\\)\u306b\u5185\u5206\u3059\u308b\u3053\u3068\u3068\u95a2\u4fc2\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u7dda\u5206DC\u3092\\(6:5\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092E\uff08\\(\\overrightarrow{OE}\\)\uff09\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305f\\(\\displaystyle\\frac{5\\overrightarrow{OD}+6\\overrightarrow{OC}}{6+5}=\\overrightarrow{OE}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OP}=\\displaystyle\\frac{11}{12}\\overrightarrow{OE}\\)<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\u7dda\u5206AB\u3092\\(2:3\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092D\u3001\u7dda\u5206DC\u3092\\(6:5\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092E\u3068\u3059\u308b\u3068\u3001\u70b9P\u306f\u7dda\u5206OE\u3092\\(11:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3067\u3042\u308b\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\/cksj6.jpg\" alt=\"\" width=\"462\" height=\"344\" class=\"aligncenter size-full wp-image-11986\" \/><\/p>\n<p>\u5185\u5206\u70b9\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3053\u3068\u3067\u70b9P\u304c\u3069\u306e\u3088\u3046\u306a\u70b9\u306a\u306e\u304b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u76f4\u7dda\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u306b\u3088\u308b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h3>\n<p>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u304c\u95a2\u308f\u308b\u8a08\u7b97\u554f\u984c\u3067\u306f\u3001\u5171\u7dda\u6761\u4ef6\u3068\u5171\u9762\u6761\u4ef6\u3092\u5229\u7528\u3059\u308b\u554f\u984c\u304c\u3072\u3093\u3071\u3093\u306b\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u7279\u306b\u5171\u9762\u6761\u4ef6\u306f\u91cd\u8981\u3067\u3042\u308a\u3001\u4fc2\u6570\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304d\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>\u56db\u9762\u4f53OABC\u306b\u3064\u3044\u3066\u3001OA\u3092\\(2:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092D\u3001OB\u3092\\(2:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092E\u3068\u3057\u307e\u3059\u3002\u25b3ABC\u306e\u91cd\u5fc3\u3092G\u3068\u3059\u308b\u3068\u304d\u3001\\(\\overrightarrow{OG}\\)\u3068\u25b3DEC\u3068\u306e\u4ea4\u70b9\u3092F\u3068\u3057\u307e\u3059\u3002\\(\\overrightarrow{OA}\\)\u3001\\(\\overrightarrow{OB}\\)\u3001\\(\\overrightarrow{OC}\\)\u3092\u7528\u3044\u3066\\(\\overrightarrow{OF}\\)\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dkdh11.jpg\" alt=\"\" width=\"334\" height=\"343\" class=\"aligncenter size-full wp-image-11867\" \/><\/p>\n<p>\u70b9G\u306f\u25b3ABC\u306e\u91cd\u5fc3\u3067\u3042\u308b\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OG}=\\displaystyle\\frac{\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}}{3}\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\\(\\overrightarrow{OF}\\)\u3092\u4f38\u3070\u3059\u3068\\(\\overrightarrow{OG}\\)\u306b\u306a\u308b\u305f\u3081\u3001\\(\\overrightarrow{OF}=k\\overrightarrow{OG}\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\overrightarrow{OF}\\)\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OF}=\\displaystyle\\frac{k}{3}\\overrightarrow{OA}+\\displaystyle\\frac{k}{3}\\overrightarrow{OB}+\\displaystyle\\frac{k}{3}\\overrightarrow{OC}\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u3001\u70b9F\u306f\u25b3DEC\u4e0a\u306b\u5b58\u5728\u3057\u307e\u3059\u3002\u305d\u3053\u3067\u5171\u9762\u6761\u4ef6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OF}=s\\overrightarrow{OD}+t\\overrightarrow{OE}+u\\overrightarrow{OC}\\)<\/li>\n<li>\\(s+t+u=1\\)<\/li>\n<\/ul>\n<p>OA\u3092\\(2:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u304cD\u3001OB\u3092\\(2:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u304cE\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OF}=\\displaystyle\\frac{2s}{3}\\overrightarrow{OA}+\\displaystyle\\frac{2t}{3}\\overrightarrow{OE}+u\\overrightarrow{OC}\\)<\/li>\n<li>\\(s+t+u=1\\)<\/li>\n<\/ul>\n<p>\u540c\u3058\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308c\u3070\u3001\u4fc2\u6570\u306f\u5fc5\u305a\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u4fc2\u6570\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OF}=\\displaystyle\\frac{k}{3}\\overrightarrow{OA}+\\displaystyle\\frac{k}{3}\\overrightarrow{OB}+\\displaystyle\\frac{k}{3}\\overrightarrow{OC}\\)<\/li>\n<li>\\(\\overrightarrow{OF}=\\displaystyle\\frac{2s}{3}\\overrightarrow{OA}+\\displaystyle\\frac{2t}{3}\\overrightarrow{OE}+u\\overrightarrow{OC}\\)<\/li>\n<\/ul>\n<p>\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{k}{3}=\\displaystyle\\frac{2s}{3}\\)<\/li>\n<li>\\(\\displaystyle\\frac{k}{3}=\\displaystyle\\frac{2t}{3}\\)<\/li>\n<li>\\(\\displaystyle\\frac{k}{3}=u\\)<\/li>\n<\/ul>\n<p>\u6574\u7406\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{k}{2}=s\\)<\/li>\n<li>\\(\\displaystyle\\frac{k}{s}=t\\)<\/li>\n<li>\\(\\displaystyle\\frac{k}{3}=u\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\\(s+t+u=1\\)\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(s+t+u=1\\)<\/p>\n<p>\\(\\displaystyle\\frac{k}{2}+\\displaystyle\\frac{k}{2}+\\displaystyle\\frac{k}{3}=1\\)<\/p>\n<p>\\(8k=6\\)<\/p>\n<p>\\(k=\\displaystyle\\frac{3}{4}\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\\(k=\\displaystyle\\frac{3}{4}\\)\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{OF}=\\displaystyle\\frac{k}{3}\\overrightarrow{OA}+\\displaystyle\\frac{k}{3}\\overrightarrow{OB}+\\displaystyle\\frac{k}{3}\\overrightarrow{OC}\\)<\/p>\n<p>\\(\\overrightarrow{OF}=\\displaystyle\\frac{1}{4}\\overrightarrow{OA}+\\displaystyle\\frac{1}{4}\\overrightarrow{OB}+\\displaystyle\\frac{1}{4}\\overrightarrow{OC}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\\overrightarrow{OA}\\)\u3001\\(\\overrightarrow{OB}\\)\u3001\\(\\overrightarrow{OC}\\)\u3092\u7528\u3044\u3066\\(\\overrightarrow{OF}\\)\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u5e73\u9762\u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068\u5e73\u9762\u3068\u306e\u4ea4\u70b9<\/h3>\n<p>\u6b21\u306b\u3001\u5782\u7dda\u3092\u7528\u3044\u308b\u5834\u5408\u306e\u8a08\u7b97\u65b9\u6cd5\u3082\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u56db\u9762\u4f53\u306b\u3064\u3044\u3066\u3001\u4e00\u3064\u306e\u9802\u70b9\u304b\u3089\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5782\u7dda\u3092\u4f5c\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/sgqj2.jpg\" alt=\"\" width=\"334\" height=\"346\" class=\"aligncenter size-full wp-image-11871\" \/><\/p>\n<p>\u3053\u306e\u56f3\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(OH\u22a5AB\\)<\/li>\n<li>\\(OH\u22a5BC\\)<\/li>\n<li>\\(OH\u22a5CA\\)<\/li>\n<\/ul>\n<p>\u5782\u76f4\u306e\u5834\u5408\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u70b9H\u306f\u70b9A\u3001\u70b9B\u3001\u70b9C\u3092\u542b\u3080\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u3082\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(OH\u22a5AH\\)<\/li>\n<\/ul>\n<p><span style=\"color: #0000ff;\">\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u5229\u7528\u3057\u3066\u30d9\u30af\u30c8\u30eb\u3092\u4f5c\u308b\u5834\u5408\u3001\u5782\u7dda\u306b\u5bfe\u3057\u3066\u5fc5\u305a\u5782\u76f4\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\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>4\u70b9O\\((0,0,0)\\)\u3001A\\((1,0,0)\\)\u3001B\\((1,1,1)\\)\u3001C\\((2,3,2)\\)\u304c\u3042\u308a\u307e\u3059\u3002\u70b9C\u304b\u3089OAB\u3092\u542b\u3080\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5782\u7dda\u3092\u5f15\u304d\u3001\u5e73\u9762\u3068\u306e\u4ea4\u70b9\u3092H\u3068\u3057\u307e\u3059\u3002\u70b9H\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/sgqj3.jpg\" alt=\"\" width=\"280\" height=\"195\" class=\"aligncenter size-full wp-image-11872\" \/><\/p>\n<p>\u3061\u306a\u307f\u306b\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u56f3\u3092\u4f5c\u308b\u3068\u304d\u3001\u56f3\u306f\u9069\u5f53\u3067\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u6b63\u78ba\u306b\u56f3\u3092\u4f5c\u308b\u306e\u306f\u6642\u9593\u304c\u304b\u304b\u308b\u305f\u3081\u3001\u4e0a\u56f3\u306e\u3088\u3046\u306a\u7c21\u4fbf\u306a\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u70b9H\u306f\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3057\u307e\u3059\u3002\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3067\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u30661\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\\(\\overrightarrow{OH}\\)\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{OH}=s\\overrightarrow{OA}+t\\overrightarrow{OB}\\)<\/p>\n<p>\\(\\overrightarrow{OH}=(s+t,t,t)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9H\u306e\u5ea7\u6a19\u306f\\((s+t,t,t)\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u306e\u305f\u3081\u3001\\(\\overrightarrow{CH}\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{CH}=(s+t-2,t-3,t-2)\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u308b\u5834\u5408\u306b\u5185\u7a4d\u304c\u30bc\u30ed\u306b\u306a\u308b\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(\\overrightarrow{CH}\u00b7\\overrightarrow{OA}=0\\)\u3088\u308a<\/strong><\/p>\n<p>\\((s+t-2)\u00d71+(t-3)\u00d70\\)\\(+(t-2)\u00d70\\)\\(=0\\)<\/p>\n<p>\\(s=2-t\\)<\/p>\n<p><strong>\u30fb\\(\\overrightarrow{CH}\u00b7\\overrightarrow{OB}=0\\)\u3088\u308a<\/strong><\/p>\n<p>\\((s+t-2)\u00d71+(t-3)\u00d71\\)\\(+(t-2)\u00d71\\)\\(=0\\)<\/p>\n<p>\\(s+3t-7=0\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\\(s=2-t\\)\u3092\\(s+3t-7=0\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(s+3t-7=0\\)<\/p>\n<p>\\((2-t)+3t-7=0\\)<\/p>\n<p>\\(2t=5\\)<\/p>\n<p>\\(t=\\displaystyle\\frac{5}{2}\\)<\/p>\n<p>\\(t=\\displaystyle\\frac{5}{2}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(s=-\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u70b9H\u306e\u5ea7\u6a19\u306f\\(\\left(2,\\displaystyle\\frac{5}{2},\\displaystyle\\frac{5}{2}\\right)\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u70b9H\u306e\u5ea7\u6a19\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u53c2\u8003\u307e\u3067\u306b\u3001\u70b9H\u306e\u5ea7\u6a19\u304c\u308f\u304b\u308c\u3070CH\u306e\u9577\u3055\uff08\\(|\\overrightarrow{CH}|\\)\uff09\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u5ea7\u6a19\u3092\u7528\u3044\u3066\u25b3OAB\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u305f\u3081\u3001\u56db\u9762\u4f53OABC\u306e\u4f53\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002CH\u306f\u5782\u7dda\u3067\u3042\u308b\u305f\u3081\u3001\u4e09\u89d2\u9310\u306e\u4f53\u7a4d\u3092\u5f97\u308b\u516c\u5f0f\u3092\u5229\u7528\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n<h2>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u554f\u984c\u3092\u89e3\u304f<\/h2>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6027\u8cea\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u540c\u3058\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u65b0\u305f\u306a\u516c\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u306a\u304a\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u5171\u9762\u6761\u4ef6\u306f\u3072\u3093\u3071\u3093\u306b\u6d3b\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u5fc5\u305a\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u8003\u3048\u65b9\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u540c\u3058\u3067\u3042\u308a\u30013\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u30011\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u30013\u70b9\u3092\u901a\u308b\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3059\u308b\u70b9\u306b\u3064\u3044\u3066\u3001\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570\u3092\u8db3\u3059\u30681\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u91cd\u8981\u306a\u306e\u306f\u3001\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3053\u3068\u306b\u3042\u308a\u307e\u3059\u3002\u70b9\u306e\u4f4d\u7f6e\u3092\u6c7a\u5b9a\u3057\u305f\u308a\u3001\u7dda\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u3092\u8a08\u7b97\u3057\u305f\u308a\u3067\u304d\u308b\u3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