{"id":11679,"date":"2022-12-18T17:36:32","date_gmt":"2022-12-18T08:36:32","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11679"},"modified":"2022-12-23T05:42:38","modified_gmt":"2022-12-22T20:42:38","slug":"vector-3","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-3.html","title":{"rendered":"\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\uff1a\u5185\u5206\u70b9\u30fb\u5916\u5206\u70b9\u30fb\u91cd\u5fc3\u3068\u5171\u7dda\u6761\u4ef6\u30fb\u5171\u70b9\u6761\u4ef6"},"content":{"rendered":"\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5b66\u3076\u5185\u5bb9\u306b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059\u3002\u539f\u70b9\u3092\u57fa\u6e96\u306b\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u8a08\u7b97\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6982\u5ff5\u306f\u5ea7\u6a19\u3068\u307b\u307c\u540c\u3058\u3067\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u306f\u539f\u70b9\u3092\u59cb\u70b9\u3068\u3059\u308b\u305f\u3081\u3001\u5ea7\u6a19\u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3053\u3068\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u56f3\u5f62\u3067\u306f\u5185\u5206\u70b9\u3084\u5916\u5206\u70b9\u3001\u91cd\u5fc3\u306a\u3069\u3082\u5b66\u3073\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u3082\u3001\u5185\u5206\u70b9\u3084\u5916\u5206\u70b9\u3001\u91cd\u5fc3\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u3067\u3059\u3002\u307e\u305f\u3001\u5229\u7528\u3059\u308b\u516c\u5f0f\u306f\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u540c\u3058\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u308a\u3001\u4e00\u3064\u306e\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u3082\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\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\u306e\u6982\u5ff5\u3084\u8a08\u7b97\u65b9\u6cd5\u3001\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u539f\u70b9\u3092\u59cb\u70b9\u3068\u3059\u308b\u30d9\u30af\u30c8\u30eb\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h2>\n<p>\u4f8b\u3048\u3070\\(\\overrightarrow{AB}\\)\u3068\u3044\u3046\u306e\u306f\u3001\u70b9A\u304b\u3089\u70b9B\u3092\u7d50\u3076\u3068\u304d\u306e\u5927\u304d\u3055\uff08\u9577\u3055\uff09\u3068\u5411\u304d\u3092\u8868\u3057\u307e\u3059\u3002\u4e00\u65b9\u3067\u539f\u70b9O\u3092\u59cb\u70b9\u3068\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3092\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u70b9A\u304c\u3042\u308b\u5834\u5408\u3001\u70b9A\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\\(\\overrightarrow{OA}\\)\u3092\u6307\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304dO\u3092\u7701\u304d\u3001\\(\\overrightarrow{a}\\)\u3068\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u8a18\u3059\u3053\u3068\u3082\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/djwh2.jpg\" alt=\"\" width=\"349\" height=\"249\" class=\"aligncenter size-full wp-image-11682\" \/><\/p>\n<p><span style=\"color: #0000ff;\">\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3046\u306e\u306f\u3001\u8981\u306f\u5ea7\u6a19\u3068\u6982\u5ff5\u304c\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/span>\u4f8b\u3048\u3070\u70b9A\\((4,3)\\)\u304c\u3042\u308b\u5834\u5408\u3001\\(\\overrightarrow{OA}=\\overrightarrow{a}=(4,3)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u4fbf\u5229\u306a\u306e\u306f\u3001\u5ea7\u6a19\u306e\u8a08\u7b97\u3068\u540c\u3058\u3088\u3046\u306b\u6271\u3048\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/djwh3.jpg\" alt=\"\" width=\"292\" height=\"230\" class=\"aligncenter size-full wp-image-11683\" \/><\/p>\n<p>\u306a\u304a\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308c\u3070\u30012\u3064\u306e\u70b9\u3092\u3064\u306a\u3050\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u3082\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(\\overrightarrow{AB}=\\overrightarrow{b}-\\overrightarrow{a}\\)\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56f3\u3092\u4f5c\u308b\u3068\u3001\\(\\overrightarrow{a}\\)\u306e\u9006\u30d9\u30af\u30c8\u30eb\u3068\\(\\overrightarrow{b}\\)\u3092\u3064\u306a\u3050\u3053\u3068\u306b\u3088\u308a\u3001\\(\\overrightarrow{AB}\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{AB}=\\overrightarrow{O\\color{red}{B}}-\\overrightarrow{O\\color{red}{A}}=\\overrightarrow{b}-\\overrightarrow{a}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/djwh4.jpg\" alt=\"\" width=\"350\" height=\"250\" class=\"aligncenter size-full wp-image-11685\" \/><\/p>\n<p>\u6570\u5b66\u3067\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u5f8c\u304b\u3089\u524d\u3092\u5f15\u304f\u3053\u3068\u3067\u7d50\u679c\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u3067\u3082\u540c\u69d8\u3067\u3042\u308a\u3001\u5f8c\u308d\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304b\u3089\u524d\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5f15\u304f\u3053\u3068\u3067\u8868\u73fe\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u308b\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9<\/h3>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u56f3\u5f62\u3067\u306e\u5ea7\u6a19\u3068\u540c\u69d8\u306b\u6271\u3048\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3082\u56f3\u5f62\u3067\u5229\u7528\u3055\u308c\u308b\u6027\u8cea\u3092\u5229\u7528\u3067\u304d\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u304c\u56f3\u5f62\u306e\u8a08\u7b97\u3067\u5229\u7528\u3055\u308c\u308b\u5185\u5206\u70b9\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(x=\\displaystyle\\frac{na+mb}{m+n}\\)<\/li>\n<\/ul>\n<p>\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u5185\u5206\u70b9\u306e\u516c\u5f0f\u306f\u3053\u308c\u3068\u540c\u3058\u3067\u3042\u308a\u3001\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\u306e\u3088\u3046\u306b\u8868\u3055\u308c\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\/dueh1.jpg\" alt=\"\" width=\"352\" height=\"249\" class=\"aligncenter size-full wp-image-11688\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #ff0000;\">\u5185\u5206\u70b9\u306e\u516c\u5f0f\u306f\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/span>\u516c\u5f0f\u304c\u540c\u3058\u7406\u7531\u306f\u5358\u7d14\u3067\u3042\u308a\u3001\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u901a\u308a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u539f\u70b9O\u3092\u59cb\u70b9\u3068\u3059\u308b\u304b\u3089\u3067\u3059\u3002\u5ea7\u6a19\u306b\u3064\u3044\u3066\u3082\u3001\u539f\u70b9O\u3092\u57fa\u6e96\u306b\u8003\u3048\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5ea7\u6a19\u5229\u7528\u3067\u3082\u30d9\u30af\u30c8\u30eb\u5229\u7528\u3067\u3082\u5185\u5206\u70b9\u306e\u516c\u5f0f\u306f\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u5185\u5206\u70b9\u306e\u516c\u5f0f\u304c\u307b\u307c\u540c\u3058\u306a\u306e\u3067\u3042\u308c\u3070\u3001\u5916\u5206\u70b9\u306e\u516c\u5f0f\u3082\u307b\u307c\u540c\u3058\u3067\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\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\/dueh2.jpg\" alt=\"\" width=\"352\" height=\"249\" class=\"aligncenter size-full wp-image-11689\" \/><\/p>\n<p>\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>\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3068\u70b9B\uff08\\(\\overrightarrow{b}\\)\uff09\u3092\u7d50\u3076\u7dda\u5206AB\u3092\\(2:1\\)\u3067\u5185\u5206\u3059\u308b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{p}\\)\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\overrightarrow{p}\\)\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\displaystyle\\frac{\\overrightarrow{a}+2\\overrightarrow{b}}{3}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odn1.jpg\" alt=\"\" width=\"350\" height=\"250\" class=\"aligncenter size-full wp-image-11695\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5185\u5206\u70b9\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u8003\u3048\u65b9\u306f\u5916\u5206\u70b9\u3082\u540c\u3058\u3067\u3059\u3002\u56f3\u5f62\u306e\u554f\u984c\u3067\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u306e\u8a08\u7b97\u304c\u3067\u304d\u308b\u5834\u5408\u3001\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h3>\n<p>\u56f3\u5f62\u3067\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u306e\u516c\u5f0f\u3092\u5b66\u3076\u3068\u304d\u3001\u540c\u6642\u306b\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3092\u5f97\u308b\u516c\u5f0f\u3082\u5b66\u3073\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u91cd\u5fc3\u3092\u5f97\u308b\u516c\u5f0f\u3082\u899a\u3048\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3092\u5f97\u308b\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)<\/li>\n<\/ul>\n<p>\u524d\u8ff0\u306e\u3068\u304a\u308a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u8003\u3048\u65b9\u306f\u5ea7\u6a19\u3068\u540c\u3058\u3067\u3059\u3002\u91cd\u5fc3\u3092\u5f97\u308b\u3068\u304d\u3001\u56f3\u5f62\u3067\u306f\\(x\\)\u5ea7\u6a19\u3068\\(y\\)\u5ea7\u6a19\u306b\u5206\u3051\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u306b\u306f\\(x\\)\u6210\u5206\u3068\\(y\\)\u6210\u5206\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u4e0a\u8a18\u306e\u516c\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u30d9\u30af\u30c8\u30eb\u6210\u5206\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u306f\\(x\\)\u6210\u5206\u3068\\(y\\)\u6210\u5206\u306b\u5206\u3051\u3066\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>A:\\(\\overrightarrow{a}=(1,1)\\)\u3001B:\\(\\overrightarrow{b}=(-3,-4)\\)\u3001C:\\(\\overrightarrow{c}=(5,7)\\)\u306b\u3064\u3044\u3066\u3001\u25b3ABC\u306e\u91cd\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30ebG:\\(\\overrightarrow{g}\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\(\\displaystyle\\frac{1-3+5}{3}=1\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\(\\displaystyle\\frac{1-4+7}{3}=\\displaystyle\\frac{4}{3}\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{g}=\\left(1,\\displaystyle\\frac{4}{3}\\right)\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u25b3ABC\u306e\u91cd\u5fc3G\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=0\\)\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3088\u308a\u3001\u91cd\u5fc3\u306f\\(\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)\u3067\u3059\u3002\u307e\u305f\\(\\overrightarrow{GA}\\)\u3001\\(\\overrightarrow{GB}\\)\u3001\\(\\overrightarrow{GC}\\)\u306f\u305d\u308c\u305e\u308c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{GA}=\\overrightarrow{a}-\\overrightarrow{g}\\)<\/li>\n<li>\\(\\overrightarrow{GB}=\\overrightarrow{b}-\\overrightarrow{g}\\)<\/li>\n<li>\\(\\overrightarrow{GC}=\\overrightarrow{c}-\\overrightarrow{g}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\\(\\overrightarrow{g}=\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)\u3092\u4ee3\u5165\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{GA}=\\displaystyle\\frac{2\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}}{3}\\)<\/li>\n<li>\\(\\overrightarrow{GB}=\\displaystyle\\frac{-\\overrightarrow{a}+2\\overrightarrow{b}-\\overrightarrow{c}}{3}\\)<\/li>\n<li>\\(\\overrightarrow{GC}=\\displaystyle\\frac{-\\overrightarrow{a}-\\overrightarrow{b}+2\\overrightarrow{c}}{3}\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}}{3}\\)\\(+\\displaystyle\\frac{-\\overrightarrow{a}+2\\overrightarrow{b}-\\overrightarrow{c}}{3}\\)\\(+\\displaystyle\\frac{-\\overrightarrow{a}-\\overrightarrow{b}+2\\overrightarrow{c}}{3}\\)<\/p>\n<p>\\(=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u8a3c\u660e\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u308b\u5171\u7dda\u6761\u4ef6<\/h2>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u308b\u8a08\u7b97\u3067\u306f\u3001\u5171\u7dda\u6761\u4ef6\u3068\u5171\u70b9\u6761\u4ef6\u3082\u91cd\u8981\u3067\u3059\u3002\u30d9\u30af\u30c8\u30eb\u306b\u306f\u5411\u304d\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u539f\u70b9O\u3092\u59cb\u70b9\u3068\u3059\u308b\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3068\u7279\u5b9a\u306e\u70b9\u3092\u6307\u5b9a\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u3060\u3051\u3067\u306a\u304f\u5834\u6240\u3082\u660e\u78ba\u306b\u6c7a\u307e\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u70b9A\u3001\u70b9B\u3001\u70b9P\u304c\u540c\u3058\u76f4\u7dda\u4e0a\u306b\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>\u3053\u308c\u304c\u5171\u7dda\u6761\u4ef6\u3067\u3059\u3002\u70b9A\u304c\u59cb\u70b9\u3067\u3042\u308a\u3001\\(\\overrightarrow{AB}\\)\u3092\u5b9f\u6570\u500d\u3057\u3066\\(k\\overrightarrow{AP}\\)\u306b\u306a\u308c\u3070\u30013\u70b9\u304c\u4e00\u3064\u306e\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3059\u308b\u306e\u306f\u5f53\u7136\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u25b3ABC\u306b\u3064\u3044\u3066\u3001\u8fbaAB\u3092\\(2:3\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092P\u3001\u8fbaAC\u3092\\(4:3\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092Q\u3001\u8fbaBC\u3092\\(2:1\\)\u306b\u5916\u5206\u3059\u308b\u70b9\u3092R\u3068\u3059\u308b\u3068\u304d\u30013\u70b9P\u3001Q\u3001R\u304c\u4e00\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5171\u7dda\u6761\u4ef6\u3088\u308a\u3001\\(\\overrightarrow{PR}=k\\overrightarrow{PQ}\\)\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\\(\\overrightarrow{PQ}\\)\u3068\\(\\overrightarrow{PR}\\)\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u56f3\u3092\u63cf\u304f\u3068\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\/odn3.jpg\" alt=\"\" width=\"490\" height=\"304\" class=\"aligncenter size-full wp-image-11700\" \/><\/p>\n<p>\u70b9A\u3001\u70b9B\u3001\u70b9C\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\\(\\overrightarrow{a}\\)\u3001\\(\\overrightarrow{b}\\)\u3001\\(\\overrightarrow{c}\\)\u3068\u3059\u308b\u3068\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\displaystyle\\frac{3\\overrightarrow{a}+2\\overrightarrow{b}}{2+3}=\\displaystyle\\frac{3\\overrightarrow{a}+2\\overrightarrow{b}}{5}\\)<\/li>\n<li>\\(\\overrightarrow{q}=\\displaystyle\\frac{3\\overrightarrow{a}+4\\overrightarrow{c}}{4+3}=\\displaystyle\\frac{3\\overrightarrow{a}+4\\overrightarrow{c}}{7}\\)<\/li>\n<li>\\(\\overrightarrow{r}=\\displaystyle\\frac{-\\overrightarrow{b}+2\\overrightarrow{c}}{2-1}=-\\overrightarrow{b}+2\\overrightarrow{c}\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\\(\\overrightarrow{PQ}\\)\u3068\\(\\overrightarrow{PR}\\)\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{PQ}=\\overrightarrow{q}-\\overrightarrow{p}\\)\\(=\\displaystyle\\frac{3\\overrightarrow{a}+4\\overrightarrow{c}}{7}-\\displaystyle\\frac{3\\overrightarrow{a}+2\\overrightarrow{b}}{5}\\)\\(=-\\displaystyle\\frac{6}{35}\\overrightarrow{a}-\\displaystyle\\frac{2}{5}\\overrightarrow{b}+\\displaystyle\\frac{4}{7}\\overrightarrow{c}\\)<\/p>\n<p>\\(\\overrightarrow{PR}=\\overrightarrow{r}-\\overrightarrow{p}\\)\\(=-\\overrightarrow{b}+2\\overrightarrow{c}-\\displaystyle\\frac{3\\overrightarrow{a}+2\\overrightarrow{b}}{5}\\)\\(=-\\displaystyle\\frac{3}{5}\\overrightarrow{a}-\\displaystyle\\frac{7}{5}\\overrightarrow{b}+2\\overrightarrow{c}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\\overrightarrow{PR}=\\displaystyle\\frac{7}{2}\\overrightarrow{PQ}\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u30813\u70b9P\u3001Q\u3001R\u306f\u4e00\u76f4\u7dda\u4e0a\u306b\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<h3>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u7b49\u3057\u3044\u3068\u5171\u70b9\u3068\u306a\u308b\uff1a\u5171\u70b9\u6761\u4ef6<\/h3>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u8a3c\u660e\u3059\u308b\u65b9\u6cd5\u306b\u5171\u70b9\u3082\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u540c\u3058\u70b9\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u7b49\u3057\u3044\u3053\u3068\u3092\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/span>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u540c\u3058\u5834\u5408\u3001\u540c\u3058\u70b9\u3092\u793a\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002\u3053\u308c\u304c\u5171\u70b9\u6761\u4ef6\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u25b3ABC\u306b\u3064\u3044\u3066\u3001\u8fbaAB\u3001BC\u3001CA\u3092\\(2:1\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092\u305d\u308c\u305e\u308cD\u3001E\u3001F\u3068\u3057\u307e\u3059\u3002\u25b3ABC\u306e\u91cd\u5fc3G\u3068\u25b3DEF\u306e\u91cd\u5fc3H\u304c\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>2\u3064\u306e\u70b9\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u56f3\u3092\u63cf\u304f\u3068\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\/odn4.jpg\" alt=\"\" width=\"447\" height=\"329\" class=\"aligncenter size-full wp-image-11704\" \/><\/p>\n<p>\u70b9D\u3001E\u3001F\u3092\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{d}=\\displaystyle\\frac{\\overrightarrow{a}+2\\overrightarrow{b}}{2+1}=\\displaystyle\\frac{\\overrightarrow{a}+2\\overrightarrow{b}}{3}\\)<\/li>\n<li>\\(\\overrightarrow{e}=\\displaystyle\\frac{\\overrightarrow{b}+2\\overrightarrow{c}}{2+1}=\\displaystyle\\frac{\\overrightarrow{b}+2\\overrightarrow{c}}{3}\\)<\/li>\n<li>\\(\\overrightarrow{f}=\\displaystyle\\frac{\\overrightarrow{c}+2\\overrightarrow{a}}{2+1}=\\displaystyle\\frac{\\overrightarrow{c}+2\\overrightarrow{a}}{3}\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\u25b3DEF\u306e\u91cd\u5fc3H\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{h}=\\displaystyle\\frac{\\displaystyle\\frac{\\overrightarrow{a}+2\\overrightarrow{b}}{3}+\\displaystyle\\frac{\\overrightarrow{b}+2\\overrightarrow{c}}{3}+\\displaystyle\\frac{\\overrightarrow{c}+2\\overrightarrow{a}}{3}}{3}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)<\/p>\n<p>\u306a\u304a\u3001\u516c\u5f0f\u3088\u308a\u25b3ABC\u306e\u91cd\u5fc3G\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\\(\\overrightarrow{g}=\\displaystyle\\frac{\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}}{3}\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\\(\\overrightarrow{g}=\\overrightarrow{h}\\)\u3068\u306a\u308a\u3001\u91cd\u5fc3G\u3068\u91cd\u5fc3H\u306f\u540c\u3058\u70b9\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3001\u5185\u5206\u70b9\u3084\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u539f\u70b9O\u3092\u57fa\u6e96\u306b\u3059\u308b\u30d9\u30af\u30c8\u30eb\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7279\u5b9a\u306e\u70b9\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u5ea7\u6a19\u3068\u307b\u307c\u540c\u3058\u6982\u5ff5\u3067\u3042\u308b\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5f97\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u91cd\u5fc3\u3092\u5f97\u308b\u3068\u304d\u3082\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u5171\u7dda\u6761\u4ef6\u3084\u5171\u70b9\u6761\u4ef6\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u540c\u4e00\u7dda\u4e0a\u306b\u70b9\u304c\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u308a\u3001\u540c\u3058\u70b9\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u308a\u3001\u70b9\u3092\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5ea7\u6a19\u3068\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u307b\u307c\u540c\u3058\u6982\u5ff5\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3044\u305f\u308a\u8a3c\u660e\u3092\u3057\u305f\u308a\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5b66\u3076\u5185\u5bb9\u306b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059\u3002\u539f\u70b9\u3092\u57fa\u6e96\u306b\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u8a08\u7b97\u3059\u308b\u306e\u3067\u3059\u3002 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