{"id":11734,"date":"2022-12-21T00:29:45","date_gmt":"2022-12-20T15:29:45","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11734"},"modified":"2022-12-24T07:46:37","modified_gmt":"2022-12-23T22:46:37","slug":"vector-5","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-5.html","title":{"rendered":"\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\uff1a\u4ea4\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb"},"content":{"rendered":"\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u76f4\u7dda\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u70b9\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u304c\u3001\u591a\u304f\u306e\u70b9\u304c\u96c6\u307e\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u76f4\u7dda\u306b\u306a\u308b\u306e\u3067\u3059\u3002\u3053\u308c\u3092\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u6570\u5b66\u3067\u306f\u3001\u95a2\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7279\u5b9a\u306e\u76f4\u7dda\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u79c1\u305f\u3061\u304c\u3053\u308c\u307e\u3067\u5b66\u3093\u3060\u95a2\u6570\u3068\u306f\u8868\u8a18\u6cd5\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u76f4\u7dda\u3092\u8868\u305b\u3070\u3044\u3044\u306e\u304b\u5b66\u3070\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u306a\u304a\u30d9\u30af\u30c8\u30eb\u304c\u95a2\u308f\u308b\u554f\u984c\u3067\u306f\u3001\u4ea4\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u3072\u3093\u3071\u3093\u306b\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u554f\u984c\u3092\u89e3\u304f\u306b\u306f\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u307e\u305f\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u306f\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\uff08\u7279\u5b9a\u306e\u7dda\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306e\u30d9\u30af\u30c8\u30eb\uff09\u3082\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u3069\u306e\u3088\u3046\u306b\u76f4\u7dda\u3092\u8868\u73fe\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u95a2\u3059\u308b\u516c\u5f0f\u3084\u554f\u984c\u306e\u89e3\u304d\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5b9a\u70b9\u3092\u901a\u308a\u3001\u7279\u5b9a\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5e73\u884c\u306a\u76f4\u7dda<\/h2>\n<p>\u95a2\u6570\u306b\u3088\u3063\u3066\u76f4\u7dda\u3092\u8868\u3059\u3068\u304d\u3001\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(y=ax+b\\)<\/li>\n<\/ul>\n<p>\u3044\u308f\u3086\u308b\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\u3001\u3053\u308c\u306b\u3088\u3063\u3066\u76f4\u7dda\u3092\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u306f\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u76f4\u7dda\u3092\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059\u306b\u306f\u3069\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3001\u76f4\u7dda\u306e\u8868\u73fe\u65b9\u6cd5\u306f\u8907\u6570\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\u3001\u300c\u5b9a\u70b9\u3092\u901a\u308a\u3001\u7279\u5b9a\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5e73\u884c\u306a\u76f4\u7dda\u300d\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u539f\u70b9O\u304c\u59cb\u70b9\u3067\u3059\u3002\u307e\u305f\u5ea7\u6a19\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u7279\u5b9a\u306e\u70b9\u3092\u8868\u3059\u306e\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u305d\u306e\u305f\u3081\\(\\overrightarrow{a}=(a_1,a_2)\\)\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u5ea7\u6a19\u4e0a\u306e\\((a_1,a_2)\\)\u3092\u8868\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\\(\\overrightarrow{a}=(4,3)\\)\u306f\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\/djwh3.jpg\" alt=\"\" width=\"292\" height=\"230\" class=\"aligncenter size-full wp-image-11683\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u5b9a\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3092\u901a\u308a\u3001\\(\\overrightarrow{0}\\)\u3067\u306f\u306a\u3044\\(\\overrightarrow{d}\\)\u306b\u5e73\u884c\u306a\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{p}\\)\u306f\u3069\u306e\u3088\u3046\u306b\u8868\u73fe\u3059\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u306b\u516c\u5f0f\u3092\u8a18\u3059\u3068\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{d}\\)<\/li>\n<\/ul>\n<p>\u203b\\(t\\)\u306f\u5b9f\u6570\u306e\u5909\u6570<\/p>\n<p>\\(\\overrightarrow{a}\\)\u306f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u5fc5\u305a\u3053\u306e\u70b9\u3092\u901a\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\\(\\overrightarrow{d}\\)\u306f\u7279\u5b9a\u306e\u5927\u304d\u3055\u3068\u5411\u304d\u3092\u3082\u3064\u30d9\u30af\u30c8\u30eb\u3067\u3059\uff08\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u306f\u306a\u3044\uff09\u3002\u305d\u306e\u305f\u3081\\(\\overrightarrow{d}\\)\u3092\\(t\\)\u500d\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7279\u5b9a\u306e\u70b9P\uff08\\(\\overrightarrow{p}\\)\uff09\u3092\u8868\u305b\u307e\u3059\u3002<\/p>\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>\u4e0a\u56f3\u3088\u308a\u3001\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{d}\\)\u3068\u306a\u308b\u306e\u306f\u554f\u984c\u306a\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\\(\\overrightarrow{p}\\)\u306f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u5927\u304d\u3055\u3068\u65b9\u5411\u3092\u3082\u3061\u307e\u3059\u304c\u3001\u524d\u8ff0\u306e\u3068\u304a\u308a\u7279\u5b9a\u306e\u70b9\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\\(t=-1,0,1,2&#8230;\\)\u3068\u4ee3\u5165\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001<span style=\"color: #ff0000;\">\u300c\\(\\overrightarrow{p}\\)\u306b\u3088\u3063\u3066\u63cf\u3051\u308b\u70b9\u300d\u3092\u3064\u306a\u3050\u3053\u3068\u3067\u76f4\u7dda\u3068\u306a\u308a\u307e\u3059\u3002<\/span><\/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>\u3053\u306e\u3088\u3046\u306b\\(\\overrightarrow{p}\\)\u304c\u70b9\u3067\u3042\u308b\u3053\u3068\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u76f4\u7dda\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u306a\u304a\u3001\\(\\overrightarrow{d}\\)\u3092\u76f4\u7dda\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3001\\(t\\)\u3092\u5a92\u4ecb\u5909\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5148\u307b\u3069\u306e\u516c\u5f0f\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>3\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3001B\uff08\\(\\overrightarrow{b}\\)\uff09\u3001C\uff08\\(\\overrightarrow{c}\\)\uff09\u304c\u9802\u70b9\u306e\u25b3ABC\u306b\u3064\u3044\u3066\u3001\u8fbaAC\u30921:3\u306b\u5185\u5206\u3059\u308b\u70b9\u3092M\u3068\u3057\u307e\u3059\u3002\u70b9M\uff08\\(\\overrightarrow{m}\\)\uff09\u3092\u901a\u308a\u3001\u8fbaAB\u306b\u5e73\u884c\u306a\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u56f3\u304c\u306a\u3044\u3068\u7406\u89e3\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u95a2\u308f\u308b\u554f\u984c\u3067\u306f\u307e\u305a\u56f3\u3092\u63cf\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb5.jpg\" alt=\"\" width=\"544\" height=\"223\" class=\"aligncenter size-full wp-image-11742\" \/><\/p>\n<p>\u6c42\u3081\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\\(\\overrightarrow{p}\\)\u3068\u3057\u307e\u3059\u3002\u70b9M\uff08\\(\\overrightarrow{m}\\)\uff09\u3092\u901a\u308a\u3001\u8fbaAB\u306b\u5bfe\u3057\u3066\u5e73\u884c\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u70b9P\uff08\\(\\overrightarrow{p}\\)\uff09\u3092\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}=\\overrightarrow{m}+t\\overrightarrow{AB}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\\(\\overrightarrow{m}\\)\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u8fbaAC\u30921:3\u306b\u5185\u5206\u3059\u308b\u70b9\u304cM\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{m}=\\displaystyle\\frac{3\\overrightarrow{a}+\\overrightarrow{c}}{1+3}=\\displaystyle\\frac{3\\overrightarrow{a}+\\overrightarrow{c}}{4}\\)<\/p>\n<p>\u6b21\u306b\u3001\\(\\overrightarrow{p}\\)\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{p}=\\overrightarrow{m}+t\\overrightarrow{AB}\\)<\/p>\n<p>\\(\\overrightarrow{p}=\\displaystyle\\frac{3\\overrightarrow{a}+\\overrightarrow{c}}{4}+t(\\overrightarrow{b}-\\overrightarrow{a})\\)<\/p>\n<p>\\(\\overrightarrow{p}=\\left(\\displaystyle\\frac{3}{4}-t\\right)\\overrightarrow{a}+t\\overrightarrow{b}+\\displaystyle\\frac{1}{4}\\overrightarrow{c}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>2\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u305d\u308c\u3067\u306f1\u70b9\u3067\u306f\u306a\u304f\u30012\u70b9\u3092\u901a\u308b\u76f4\u7dda\u3092\u8868\u73fe\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3001\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3068\u70b9B\uff08\\(\\overrightarrow{b}\\)\uff09\u3092\u901a\u308b\u76f4\u7dda\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb12.jpg\" alt=\"\" width=\"441\" height=\"179\" class=\"aligncenter size-full wp-image-11749\" \/><\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u70b9A\u3092\u901a\u308a\u3001\u8fbaAB\u306b\u5bfe\u3057\u3066\u5e73\u884c\u306a\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{p}\\)\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{AB}\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\\(\\overrightarrow{AB}=\\overrightarrow{OB}-\\overrightarrow{OA}=\\overrightarrow{b}-\\overrightarrow{a}\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{p}=\\overrightarrow{a}+t\\overrightarrow{AB}\\)<\/p>\n<p>\\(\\overrightarrow{p}=\\overrightarrow{a}+t(\\overrightarrow{b}-\\overrightarrow{a})\\)<\/p>\n<p>\\(\\overrightarrow{p}=(1-t)\\overrightarrow{a}+t\\overrightarrow{b}\\)<\/p>\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>\u3053\u3046\u3057\u3066\u30012\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\\(\\overrightarrow{p}=(1-t)\\overrightarrow{a}+t\\overrightarrow{b}\\)\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3057\u305f\u3002\u305d\u308c\u3067\u306f\u3001\u3053\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>2\u70b9\u3001A\\((1,2)\\)\u3068B\\((3,5)\\)\u3092\u901a\u308b\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u5a92\u4ecb\u5909\u6570\\(t\\)\u3092\u7528\u3044\u3066\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u5ea7\u6a19\u3068\u540c\u3058\u3088\u3046\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u70b9P\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\\(\\overrightarrow{p}=(x,y)\\)\u3068\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{p}=(1-t)\\overrightarrow{OA}+t\\overrightarrow{OB}\\)<\/p>\n<p>\\((x,y)=(1-t)(1,2)+t(3,5)\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb9.jpg\" alt=\"\" width=\"349\" height=\"291\" class=\"aligncenter size-full wp-image-11746\" \/><\/p>\n<p>\u305d\u3053\u3067\u3001\\(x\\)\u6210\u5206\u3068\\(y\\)\u6210\u5206\u306b\u5206\u3051\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x=2t+1\\)<\/li>\n<li>\\(y=3t+2\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\\overrightarrow{p}=(2t+1,3t+2)\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u53c2\u8003\u307e\u3067\u306b\u3001\\(x=2t+1\\)\u3068\\(y=3t+2\\)\u3092\u7528\u3044\u3066\\(t\\)\u3092\u6d88\u3059\u3068\\(3x-2y+1=0\\)\u306b\u306a\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u76f4\u7dda\u3092\u8868\u3059\u305f\u3081\u3001\u5a92\u4ecb\u5909\u6570\u3092\u7528\u3044\u306a\u3044\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<h4>\u4ea4\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u65b9\u6cd5<\/h4>\n<p>\u306a\u304a\u3001\u30d9\u30af\u30c8\u30eb\u304c\u95a2\u308f\u308b\u554f\u984c\u3067\u6700\u3082\u51fa\u984c\u3055\u308c\u308b\u5185\u5bb9\u306e\u4e00\u3064\u304c\u4ea4\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u4ea4\u70b9\u3092\u8868\u3059\u3068\u304d\u3001\\(\\overrightarrow{p}=(1-t)\\overrightarrow{a}+t\\overrightarrow{b}\\)\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u3059\u3002\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>\u25b3OAB\u306b\u3064\u3044\u3066\u3001\u8fbaOA\u3092\\(1:3\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092C\u3001\u8fbaOB\u3092\\(1:5\\)\u306b\u5185\u5206\u3059\u308b\u70b9\u3092D\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u7dda\u5206AD\u3068BC\u306e\u4ea4\u70b9\u3092P\u3001\u76f4\u7ddaOP\u3068\u8fbaAB\u3068\u306e\u4ea4\u70b9\u3092Q\u3068\u3057\u307e\u3059\u3002\\(\\overrightarrow{OP}\\)\u3068\\(\\overrightarrow{OQ}\\)\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{OA}=\\overrightarrow{a}\\)\u3068\\(\\overrightarrow{OB}=\\overrightarrow{b}\\)\u3092\u7528\u3044\u3066\u8868\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\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\/odjwb8.jpg\" alt=\"\" width=\"421\" height=\"271\" class=\"aligncenter size-full wp-image-11745\" \/><\/p>\n<p>\\(\\overrightarrow{OP}\\)\u30922\u3064\u306e\u5a92\u4ecb\u5909\u6570\uff08\\(s,t\\)\uff09\u3092\u5229\u7528\u3057\u3066\u8868\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3088\u3063\u3066\u76f4\u7dda\u3092\u8868\u3057\u305f\u5f8c\u3001\u5a92\u4ecb\u5909\u6570\u3092\u6d88\u3059\u3053\u3068\u3067\\(\\overrightarrow{OP}\\)\u3092\u5f97\u308b\u306e\u3067\u3059\u3002\u4e0a\u56f3\u306e\u3088\u3046\u306b\u5a92\u4ecb\u5909\u6570\u3092\u5229\u7528\u3059\u308b\u3068\u3001\\(\\overrightarrow{OP}\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OP}=t\\overrightarrow{OD}+(1-t)\\overrightarrow{OA}\\)\\(=\\displaystyle\\frac{1}{6}t\\overrightarrow{b}+(1-t)\\overrightarrow{a}\\)<\/li>\n<li>\\(\\overrightarrow{OP}=s\\overrightarrow{OC}+(1-s)\\overrightarrow{OB}\\)\\(=\\displaystyle\\frac{1}{4}s\\overrightarrow{a}+(1-s)\\overrightarrow{b}\\)<\/li>\n<\/ul>\n<p><span style=\"color: #0000ff;\">\u540c\u3058\u30d9\u30af\u30c8\u30eb\uff08\\(\\overrightarrow{OP}\\)\uff09\u3067\u3042\u308b\u305f\u3081\u3001\u4fc2\u6570\u306f\u5fc5\u305a\u4e00\u81f4\u3057\u307e\u3059\u3002<\/span>\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{1}{6}t=1-s\\)<\/li>\n<li>\\(\\displaystyle\\frac{1}{4}s=1-t\\)<\/li>\n<\/ul>\n<p>\\(\\displaystyle\\frac{1}{6}t=1-s\\)\u3088\u308a\u3001\\(t=6-6s\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{4}s=1-t\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{4}s=1-(6-6s)\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{4}s=-5+6s\\)<\/p>\n<p>\\(s=-20+24s\\)<\/p>\n<p>\\(-23s=-20\\)<\/p>\n<p>\\(s=\\displaystyle\\frac{20}{23}\\)<\/p>\n<p>\u305d\u3053\u3067\\(\\overrightarrow{OP}=\\displaystyle\\frac{1}{4}s\\overrightarrow{a}+(1-s)\\overrightarrow{b}\\)\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\\(\\overrightarrow{OP}\\)\\(=\\displaystyle\\frac{5}{23}\\overrightarrow{a}+\\displaystyle\\frac{3}{23}\\overrightarrow{b}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\\(\\overrightarrow{OP}\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p><strong>\u30fb\\(\\overrightarrow{OQ}\\)\u3092\u8a08\u7b97\u3059\u308b<\/strong><\/p>\n<p>\u8003\u3048\u65b9\u306f\u5148\u307b\u3069\u3068\u540c\u3058\u3067\u3042\u308a\u3001\\(\\overrightarrow{OQ}\\)\u30922\u901a\u308a\u306e\u65b9\u6cd5\u3067\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u56f3\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odjwb14.jpg\" alt=\"\" width=\"404\" height=\"264\" class=\"aligncenter size-full wp-image-11752\" \/><\/p>\n<p>\u4e0a\u56f3\u306e\u3088\u3046\u306b\u5a92\u4ecb\u5909\u6570\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\overrightarrow{OQ}\\)\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OQ}=(1-u)\\overrightarrow{a}+u\\overrightarrow{b}\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\\(\\overrightarrow{OP}\\)\u3092\u4f38\u3070\u3059\u3068\\(\\overrightarrow{OQ}\\)\u306b\u306a\u308b\u305f\u3081\u3001\\(\\overrightarrow{OP}\\)\\(=k\\overrightarrow{OQ}\\)\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\\(\\overrightarrow{OP}=\\displaystyle\\frac{5}{23}\\overrightarrow{a}+\\displaystyle\\frac{3}{23}\\overrightarrow{b}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{OQ}=\\displaystyle\\frac{5}{23}k\\overrightarrow{a}+\\displaystyle\\frac{3}{23}k\\overrightarrow{b}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4fc2\u6570\u6bd4\u8f03\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(1-u=\\displaystyle\\frac{5}{23}k\\)<\/li>\n<li>\\(u=\\displaystyle\\frac{3}{23}k\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(1-u=\\displaystyle\\frac{5}{23}k\\)<\/p>\n<p>\\(1-\\displaystyle\\frac{3}{23}k=\\displaystyle\\frac{5}{23}k\\)<\/p>\n<p>\\(1=\\displaystyle\\frac{8}{23}k\\)<\/p>\n<p>\\(k=\\displaystyle\\frac{23}{8}\\)<\/p>\n<p>\\(k=\\displaystyle\\frac{23}{8}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\\overrightarrow{OQ}=\\displaystyle\\frac{5}{23}k\\overrightarrow{a}+\\displaystyle\\frac{3}{23}k\\overrightarrow{b}\\)\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\\(\\overrightarrow{OQ}=\\displaystyle\\frac{5}{8}\\overrightarrow{a}+\\displaystyle\\frac{3}{8}\\overrightarrow{b}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\\(\\overrightarrow{OQ}\\)\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u5b9a\u70b9\u3092\u901a\u308a\u3001\u7279\u5b9a\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5782\u76f4\u306e\u76f4\u7dda\uff1a\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb<\/h3>\n<p>\u76f4\u89d2\u306e\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u8868\u3059\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u7279\u5b9a\u306e\u7dda\u306b\u5bfe\u3057\u3066\u3001\u5782\u76f4\u306a\u7dda\u3092\u6cd5\u7dda\u3068\u3044\u3044\u307e\u3059\u3002\u6cd5\u7dda\u304c\u5927\u304d\u3055\u3068\u5411\u304d\u3092\u3082\u3064\u5834\u5408\u3001<span style=\"color: #ff0000;\">\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u300c\u5b9a\u70b9A\uff08\\(\\overrightarrow{a}\\)\uff09\u3092\u901a\u308a\u3001\\(\\overrightarrow{0}\\)\u3067\u306f\u306a\u3044\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{n}\\)\u306b\u5782\u76f4\u306e\u76f4\u7dda\u300d\u3092\u3069\u306e\u3088\u3046\u306b\u8868\u305b\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u7279\u5b9a\u306e\u70b9\u3092P\uff08\\(\\overrightarrow{p}\\)\uff09\u3068\u3059\u308b\u3068\u3001\\(\\overrightarrow{AP}\\)\u306f\u70b9A\u304b\u3089\u70b9P\u3092\u7d50\u3076\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u70b9A\u3092\u901a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u3001\u70b9P\u306e\u5834\u6240\u306b\u3088\u3063\u3066\\(\\overrightarrow{AP}\\)\u306e\u5411\u304d\u306f\u3055\u307e\u3056\u307e\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(\\overrightarrow{AP}\u00b7\\overrightarrow{n}=0\\)\u3068\u306a\u308b\u6761\u4ef6\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<span style=\"color: #0000ff;\">2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u306e\u5834\u5408\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u307e\u305f\\(\\overrightarrow{AP}=\\overrightarrow{OP}-\\overrightarrow{OA}\\)\\(=\\overrightarrow{p}-\\overrightarrow{a}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\overrightarrow{AP}\u00b7\\overrightarrow{n}=0\\)\u3092\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((\\overrightarrow{p}-\\overrightarrow{a})\u00b7\\overrightarrow{n}=0\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/efje6.jpg\" alt=\"\" width=\"545\" height=\"200\" class=\"aligncenter size-full wp-image-11780\" 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