{"id":11817,"date":"2022-12-23T16:05:24","date_gmt":"2022-12-23T07:05:24","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11817"},"modified":"2022-12-27T07:55:07","modified_gmt":"2022-12-26T22:55:07","slug":"vector-8","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-8.html","title":{"rendered":"\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\uff1a\u7a7a\u9593\u5ea7\u6a19\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5206\u89e3\u3001\u8ddd\u96e2\u3001\u5e73\u884c\u6761\u4ef6"},"content":{"rendered":"\n<p>\u30d9\u30af\u30c8\u30eb\u3092\u5b66\u3076\u3068\u304d\u3001\u79c1\u305f\u3061\u304c\u6700\u521d\u306b\u7fd2\u3046\u306e\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306e2\u3064\u3092\u8003\u3048\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u4e00\u65b9\u3067\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u7acb\u4f53\u306b\u306a\u308b\u305f\u3081\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306b\u52a0\u3048\u3066\\(z\\)\u8ef8\u3092\u8003\u616e\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305f\u3060\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u30d9\u30af\u30c8\u30eb\u306e\u6982\u5ff5\u306f\u540c\u3058\u3067\u3059\u3057\u3001\u5229\u7528\u3059\u308b\u516c\u5f0f\u3082\u307b\u307c\u540c\u3058\u3067\u3059\u3002\u5f53\u7136\u3001\u8a08\u7b97\u65b9\u6cd5\u3082\u9055\u3044\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u3064\u307e\u308a\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306f\u307b\u307c\u540c\u3058\u6982\u5ff5\u3068\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u304c\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3057\u3066\u3044\u308c\u3070\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u308b\u7406\u7531\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7acb\u4f53\u56f3\u5f62\u3067\u306e\u30d9\u30af\u30c8\u30eb\u306f\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7a7a\u9593\u5ea7\u6a19\u30842\u70b9\u9593\u306e\u8ddd\u96e2\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5206\u89e3\u3001\u5e73\u884c\u6761\u4ef6\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6700\u5c0f\u5024\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u5ea7\u6a19\u3068\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u306e\u9055\u3044<\/h2>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306e2\u65b9\u5411\u3092\u8003\u3048\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4e8c\u6b21\u5143\u3067\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u4e00\u65b9\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\\(x\\)\u8ef8\u3001\\(y\\)\u8ef8\u3001\\(z\\)\u8ef8\u306e3\u65b9\u5411\u3067\u8003\u3048\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4e09\u6b21\u5143\u3067\u8a08\u7b97\u3059\u308b\u306e\u304c\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u4e09\u6b21\u5143\u3067\u3042\u308b\u305f\u3081\u3001\u7279\u5b9a\u306e\u70b9P\u3092\u8868\u3059\u3068\u304d\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\\(\\overrightarrow{p}=(x,y,z)\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{p}=(x,y)\\)\u306b\u6bd4\u3079\u3066\u3001\u8a18\u3059\u3079\u304d\u5ea7\u6a19\u304c\u4e00\u3064\u5897\u3048\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/idhd1.jpg\" alt=\"\" width=\"600\" height=\"241\" class=\"aligncenter size-full wp-image-11829\" \/><\/p>\n<p>\u306a\u304a\u4e00\u822c\u7684\u306b\u306f\u3001\u70b9A\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\\(\\overrightarrow{a}=(a_1,a_2,a_3)\\)\u3068\u8a18\u3057\u307e\u3059\u3002\\(x\\)\u6210\u5206\u304c\\(a_1\\)\u3001\\(y\\)\u6210\u5206\u304c\\(a_2\\)\u3001\\(z\\)\u6210\u5206\u304c\\(a_3\\)\u3067\u3059\u3002<\/p>\n<h3>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u540c\u3058<\/h3>\n<p>\u524d\u8ff0\u306e\u901a\u308a\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u307b\u307c\u540c\u3058\u3067\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5229\u7528\u3067\u304d\u308b\u8a08\u7b97\u6cd5\u306f\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u4ea4\u63db\u6cd5\u5247\uff1a\\(\\overrightarrow{a}+\\overrightarrow{b}=\\overrightarrow{b}+\\overrightarrow{a}\\)<\/li>\n<li>\u7d50\u5408\u6cd5\u5247\uff1a\\((\\overrightarrow{a}+\\overrightarrow{b})+\\overrightarrow{c}\\)\\(=\\overrightarrow{a}+(\\overrightarrow{b}+\\overrightarrow{c})\\)<\/li>\n<li>\u30bc\u30ed\u30d9\u30af\u30c8\u30eb\uff1a\\(\\overrightarrow{AA}=\\overrightarrow{0}=|\\overrightarrow{0}|\\)<\/li>\n<li>\u9006\u30d9\u30af\u30c8\u30eb\uff1a\\(\\overrightarrow{a}-\\overrightarrow{a}=\\overrightarrow{0}\\)<\/li>\n<li>0\u306e\u6027\u8cea\uff1a\\(\\overrightarrow{a}-\\overrightarrow{0}=\\overrightarrow{a}\\)<\/li>\n<li>\u5b9f\u6570\u500d\uff1a\\(k(\\overrightarrow{a}+\\overrightarrow{b})=k\\overrightarrow{b}+k\\overrightarrow{a}\\)<\/li>\n<li>\u5b9f\u6570\u500d\uff1a\\((k+l)\\overrightarrow{a}=k\\overrightarrow{a}+l\\overrightarrow{a}\\)<\/li>\n<li>\u5b9f\u6570\u500d\uff1a\\(k(l\\overrightarrow{a})=kl\\overrightarrow{a}\\)<\/li>\n<\/ul>\n<p>\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3001\u5b9f\u6570\u500d\u3092\u3059\u308b\u3068\u304d\u3001\u3084\u308a\u65b9\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3082\u540c\u3058\u3067\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5206\u89e3\u3068\u6210\u5206\u8868\u793a<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u6210\u5206\u8868\u793a\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3001\u5b9f\u6570\u500d\u3092\u3059\u308b\u3068\u304d\u3001\u6210\u5206\u3054\u3068\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u70b9A\uff1a\\(\\overrightarrow{a}=(a_1,a_2,a_3)\\)\u3068\u70b9B\uff1a\\(\\overrightarrow{b}=(b_1,b_2,b_3)\\)\u304c\u3042\u308b\u3068\u304d\u3001\u8db3\u3057\u7b97\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\(a_1+b_1\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\(a_2+b_2\\)<\/li>\n<li>\\(z\\)\u6210\u5206\uff1a\\(a_3+b_3\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\u5f15\u304d\u7b97\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\(a_1-b_1\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\(a_2-b_2\\)<\/li>\n<li>\\(z\\)\u6210\u5206\uff1a\\(a_3-b_3\\)<\/li>\n<\/ul>\n<p><span class=\"note\">\\(\\overrightarrow{a}\\)\u3092\u5b9f\u6570\u500d\uff08\\(k\\)\uff09\u3059\u308b\u5834\u5408\u3067\u3042\u308c\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\(ka_1\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\(ka_2\\)<\/li>\n<li>\\(z\\)\u6210\u5206\uff1a\\(ka_3\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u8a08\u7b97\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u307b\u307c\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5206\u89e3<\/strong><\/p>\n<p>\u306a\u304a\u30011\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308c\u3070\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u30661\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jd9.jpg\" alt=\"\" width=\"299\" height=\"113\" class=\"aligncenter size-full wp-image-11639\" \/><\/p>\n<p>\u3053\u306e\u5834\u5408\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5b9f\u6570\u500d\u3057\u305f\u5f8c\u3001\u3064\u306a\u3050\u3053\u3068\u306b\u3088\u3063\u30661\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e0a\u56f3\u3067\u3042\u308c\u3070\\(\\overrightarrow{b}\\)\u3092\\(k\\)\u500d\u3001\\(\\overrightarrow{c}\\)\u3092\\(l\\)\u500d\u3059\u308b\u3053\u3068\u3067\\(\\overrightarrow{a}\\)\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}=k\\overrightarrow{b}+l\\overrightarrow{c}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jd10.jpg\" alt=\"\" width=\"259\" height=\"146\" class=\"aligncenter size-full wp-image-11640\" \/><\/p>\n<p>\u4e00\u65b9\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3001\\(z\\)\u6210\u5206\u306e3\u3064\u3092\u8003\u616e\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u305d\u3053\u3067<span style=\"color: #0000ff;\">\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3067\u306f\u306a\u304f\u30013\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u5206\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/span>\u4f8b\u3048\u3070\\(\\overrightarrow{a}\\)\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{b}\\)\u3001\\(\\overrightarrow{c}\\)\u3001\\(\\overrightarrow{d}\\)\u3068\u5b9f\u6570\\(s,t,u\\)\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}=s\\overrightarrow{b}+t\\overrightarrow{c}+u\\overrightarrow{d}\\)<\/li>\n<\/ul>\n<p>\\(z\\)\u6210\u5206\u304c\u5897\u3048\u308b\u305f\u3081\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3057\u3066\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u3092\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5e73\u884c\u6761\u4ef6\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb<\/h3>\n<p>\u5e73\u884c\u6761\u4ef6\u306b\u3064\u3044\u3066\u3082\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u8003\u3048\u65b9\u304c\u540c\u3058\u3067\u3059\u3002\u30d9\u30af\u30c8\u30eb\u304c\u5e73\u884c\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}=k\\overrightarrow{b}\\)<\/li>\n<\/ul>\n<p>\u5b9f\u6570\u500d\u3059\u308b\u3053\u3068\u3067\u540c\u3058\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308b\u5834\u5408\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u5e73\u884c\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a<span style=\"color: #0000ff;\">2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5e73\u884c\u306e\u5834\u5408\u3001\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3001\\(z\\)\u6210\u5206\u306e\u6bd4\u306f\u305d\u308c\u305e\u308c\u540c\u3058\u3067\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\\(\\overrightarrow{a}=(a_1,a_2,a_3)\\)\u3068\\(\\overrightarrow{b}=(b_1,b_2,b_3)\\)\u304c\u5e73\u884c\u306a\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_1:a_2=b_1:b_2\\) \u2192 \\(a_1b_2=a_2b_1\\)<\/li>\n<li>\\(a_2:a_3=b_2:b_3\\) \u2192 \\(a_2b_3=a_3b_2\\)<\/li>\n<li>\\(a_3:a_1=b_3:b_1\\) \u2192 \\(a_3b_1=a_1b_3\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u5e73\u884c\u306a\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_1b_2-a_2b_1=0\\)<\/li>\n<li>\\(a_2b_3-a_3b_2=0\\)<\/li>\n<li>\\(a_3b_1-a_1b_3=0\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u304c\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5e73\u884c\u6761\u4ef6\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>\\(\\overrightarrow{a}=(2,3,-4)\\)\u306e\u3068\u304d\u3001\\(\\overrightarrow{a}\\)\u3068\u53cd\u5bfe\u5411\u304d\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7acb\u4f53\u56f3\u5f62\u3067\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u30013\u3064\u306e\u8fba\u3092\u4e8c\u4e57\u3057\u305f\u5f8c\u3001\u5e73\u65b9\u6839\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dvn13.jpg\" alt=\"\" width=\"600\" height=\"241\" class=\"aligncenter size-full wp-image-11926\" \/><\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\\overrightarrow{a}\\)\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(|\\overrightarrow{a}|=\\sqrt{2^2+3^2+(-4)^2}\\)<\/p>\n<p>\\(|\\overrightarrow{a}|=\\sqrt{29}\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\\(\\overrightarrow{a}\\)\u306b\u5bfe\u3057\u3066\\(\\displaystyle\\frac{1}{\\sqrt{29}}\\)\u500d\u3059\u308c\u3070\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002\u306a\u304a\\(\\overrightarrow{a}\\)\u3068\u53cd\u5bfe\u5411\u304d\u306b\u3059\u308b\u305f\u3081\u306b\u306f\u3001\\(-1\\)\u500d\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(\\overrightarrow{a}\\)\u306b\u5bfe\u3057\u3066\\(-\\displaystyle\\frac{1}{\\sqrt{29}}\\)\u500d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u306e\u7d50\u679c\u3001\u7b54\u3048\u306f\\(-\\displaystyle\\frac{1}{\\sqrt{29}}\\overrightarrow{a}=\\left(-\\displaystyle\\frac{2}{\\sqrt{29}},-\\displaystyle\\frac{3}{\\sqrt{29}},\\displaystyle\\frac{4}{\\sqrt{29}}\\right)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u5e73\u884c\u306a\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\u5b9f\u6570\u500d\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>2\u70b9\u9593\u306e\u8ddd\u96e2\u3068\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6700\u5c0f\u5024<\/h3>\n<p>1\u3064\u306e\u70b9\u306b\u3064\u3044\u3066\u8ddd\u96e2\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3089\u3001\u6b21\u306f2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u30d9\u30af\u30c8\u30eb\u306e\u6982\u5ff5\u306f\u5ea7\u6a19\u3068\u307b\u307c\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306e\u5834\u5408\u3068\u8003\u3048\u65b9\u306f\u540c\u3058\u3067\u3059\u3002\u4f8b\u3048\u3070\\(\\overrightarrow{AB}\\)\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u3068\u3044\u3046\u306e\u306f\u3001\u7dda\u5206AB\u306e\u9577\u3055\u3092\u8a08\u7b97\u3059\u308b\u306e\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u7a7a\u9593\u4e0a\u30672\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3001\\(z\\)\u6210\u5206\u3067\u305d\u308c\u305e\u308c\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5f8c\u304b\u3089\u524d\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u306e\u8ddd\u96e2\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\\(\\overrightarrow{AB}\\)\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\(b_1-a_1\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\(b_2-a_2\\)<\/li>\n<li>\\(z\\)\u6210\u5206\uff1a\\(b_3-a_3\\)<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{AB}=(b_1-a_1,b_2-a_2,b_3-a_3)\\)<\/li>\n<\/ul>\n<p>\\(\\overrightarrow{AB}=\\overrightarrow{b}-\\overrightarrow{a}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u3088\u3046\u306a\u8a08\u7b97\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\\(\\overrightarrow{AB}\\)\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(|\\overrightarrow{AB}|=\\)\\(\\sqrt{(b_1-a_1)^2+(b_2-a_2)^2+(b_3-a_3)^2}\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u304c\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u30672\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u5f97\u308b\u516c\u5f0f\u3067\u3059\u3002\u7a7a\u9593\u56f3\u5f62\u3067\u8ddd\u96e2\u3092\u5f97\u308b\u65b9\u6cd5\u3068\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u516c\u5f0f\u3092\u899a\u3048\u306a\u304f\u3066\u3082\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u306e\u8a08\u7b97\u306f\u5bb9\u6613\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>\\(\\overrightarrow{a}=(0,2,4)\\)\u3001\\(\\overrightarrow{b}=(1,0,1)\\)\u306e\u3068\u304d\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|\\)\u304c\u6700\u5c0f\u306b\u306a\u308b\\(t\\)\u3068\u305d\u306e\u3068\u304d\u306e\u5927\u304d\u3055\uff08\u9577\u3055\uff09\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|\\)\u3092\u4e8c\u4e57\u3057\u307e\u3057\u3087\u3046\u3002\\(|\\overrightarrow{a}-t\\overrightarrow{b}|\u22670\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|^2\\)\u304c\u6700\u5c0f\u306e\u5834\u5408\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|\\)\u3082\u6700\u5c0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\\(\\overrightarrow{a}-t\\overrightarrow{b}\\)\u3092\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}-t\\overrightarrow{b}=(-t,2,4-t)\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\\(\\overrightarrow{a}-t\\overrightarrow{b}\\)\u306e\u8ddd\u96e2\u306e\u4e8c\u4e57\uff08\\(|\\overrightarrow{a}-t\\overrightarrow{b}|^2\\)\uff09\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(|\\overrightarrow{a}-t\\overrightarrow{b}|^2\\)<\/p>\n<p>\\(=(-t)^2+2^2+(4-t)^2\\)<\/p>\n<p>\\(=t^2+4+(t^2-8t+16)\\)<\/p>\n<p>\\(=2t^2-8t+20\\)<\/p>\n<p>\\(=2(t^2-4t)+20\\)<\/p>\n<p>\\(=2(t-2)^2+12\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(t=2\\)\u306e\u3068\u304d\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|^2\\)\u306e\u6700\u5c0f\u5024\u306f12\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\\(t=2\\)\u306e\u3068\u304d\u3001\\(|\\overrightarrow{a}-t\\overrightarrow{b}|\\)\u306e\u6700\u5c0f\u5024\u306f\\(2\\sqrt{3}\\)\u3067\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u57fa\u672c\u3092\u7406\u89e3\u3059\u308b<\/h2>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u3001\\(z\\)\u6210\u5206\u3092\u52a0\u3048\u308b\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u9055\u3044\u306f\u3001\\(z\\)\u6210\u5206\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3067\u3042\u308b\u305f\u3081\u3001\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u306e\u8003\u3048\u65b9\u3084\u516c\u5f0f\u306f\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3001\u5b9f\u6570\u500d\u3092\u3059\u308b\u3068\u304d\u3001\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u306b\u308f\u3051\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5e73\u884c\u3068\u306a\u308b\u5834\u5408\u3001\u5b9f\u6570\u500d\u3059\u308b\u3068\u540c\u3058\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a2\u70b9\u9593\u306e\u8ddd\u96e2\uff08\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\uff09\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u5ea7\u6a19\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u5b66\u3076\u3068\u304d\u3001\u3053\u308c\u3089\u57fa\u672c\u7684\u306a\u5185\u5bb9\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3084\u5ea7\u6a19\u3092\u7528\u3044\u3066\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3093\u3067\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3092\u7406\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30d9\u30af\u30c8\u30eb\u3092\u5b66\u3076\u3068\u304d\u3001\u79c1\u305f\u3061\u304c\u6700\u521d\u306b\u7fd2\u3046\u306e\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306e2\u3064\u3092\u8003\u3048\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u4e00\u65b9\u3067\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u7acb\u4f53\u306b\u306a\u308b\u305f\u3081\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306b\u52a0\u3048\u3066\\(z\\)\u8ef8\u3092\u8003\u616e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11833,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11817","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11817","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=11817"}],"version-history":[{"count":9,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11817\/revisions"}],"predecessor-version":[{"id":11932,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11817\/revisions\/11932"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11833"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11817"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11817"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11817"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}