{"id":11836,"date":"2022-12-24T15:22:43","date_gmt":"2022-12-24T06:22:43","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11836"},"modified":"2022-12-28T05:10:44","modified_gmt":"2022-12-27T20:10:44","slug":"vector-9","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-9.html","title":{"rendered":"\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\uff1a\u516c\u5f0f\u3084\u89d2\u5ea6\u30fb\u9762\u7a4d\u306e\u8a08\u7b97\u3001\u5782\u76f4\u3067\u306e\u5185\u7a4d"},"content":{"rendered":"\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u8a08\u7b97\u3068\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u6982\u5ff5\u306f\u540c\u3058\u3067\u3059\u3002\u516c\u5f0f\u3082\u307b\u307c\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5185\u7a4d\u3092\u7406\u89e3\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3059\u3002<\/p>\n<p>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u89d2\u5ea6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u4ed6\u306b\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u306e\u5834\u5408\u3001\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6027\u8cea\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u3092\u5229\u7528\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u5185\u7a4d\u306e\u516c\u5f0f\u3084\u89d2\u5ea6\u30fb\u9762\u7a4d\u306e\u8a08\u7b97\u65b9\u6cd5\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u3068\u306a\u308b\u5834\u5408\u306e\u8003\u3048\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u3092\u5f97\u308b\u516c\u5f0f<\/h2>\n<p>\u89d2\u5ea6\u3092\u5229\u7528\u3057\u3066\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3082\u516c\u5f0f\u306f\u540c\u3058\u3067\u3059\u3002<span style=\"color: #3366ff;\">2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u3001cos\u03b8\u3092\u7528\u3044\u3066\u5411\u304d\u3092\u540c\u3058\u306b\u3057\u305f\u3042\u3068\u3001\u9577\u3055\u3092\u304b\u3051\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5185\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}=|\\overrightarrow{a}||\\overrightarrow{b}|cos\u03b8\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/odkw2.jpg\" alt=\"\" width=\"497\" height=\"192\" class=\"aligncenter size-full wp-image-11664\" \/><\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3082\u3001\u89d2\u5ea6\u3092\u5229\u7528\u3057\u3066\u5185\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u4e8b\u5b9f\u306f\u540c\u3058\u3067\u3059\u3002<\/p>\n<h3>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u6027\u8cea<\/h3>\n<p>\u307e\u305f\u5185\u7a4d\u306e\u6027\u8cea\u306b\u3064\u3044\u3066\u3082\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u540c\u3058\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u4ea4\u63db\u6cd5\u5247\uff1a\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}=\\overrightarrow{b}\u00b7\\overrightarrow{a}\\)<\/li>\n<li>\u5206\u914d\u6cd5\u5247\uff1a\\(\\overrightarrow{a}(\\overrightarrow{b}+\\overrightarrow{c})=\\overrightarrow{a}\u00b7\\overrightarrow{b}\\)\\(+\\overrightarrow{a}\u00b7\\overrightarrow{c}\\)<\/li>\n<li>\u5b9f\u6570\u500d\uff1a\\(k\\overrightarrow{a}(\\overrightarrow{b})=\\overrightarrow{a}(k\\overrightarrow{b})\\)\\(=k(\\overrightarrow{a}\u00b7\\overrightarrow{b})\\)<\/li>\n<li>\u540c\u3058\u30d9\u30af\u30c8\u30eb\uff1a\\(\\overrightarrow{a}\u00b7\\overrightarrow{a}=|\\overrightarrow{a}|^2\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\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>\u8fba\u306e\u9577\u3055\u304c1\u3067\u3042\u308b\u6b63\u56db\u9762\u4f53OABC\u306b\u3064\u3044\u3066\u3001\\(\\overrightarrow{OA}=\\overrightarrow{a}\\)\u3001\\(\\overrightarrow{OB}=\\overrightarrow{b}\\)\u3001\\(\\overrightarrow{OC}=\\overrightarrow{c}\\)\u3067\u3042\u308a\u3001\u8fbaBC\u4e0a\u306b\\(BD=\\displaystyle\\frac{1}{4}BC\\)\u3068\u306a\u308b\u70b9D\u3092\u4f5c\u308a\u307e\u3059\u3002\u5185\u7a4d\\(\\overrightarrow{OA}\u00b7\\overrightarrow{OD}\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u30d9\u30af\u30c8\u30eb\u306b\u95a2\u3059\u308b\u8a08\u7b97\u554f\u984c\u3067\u306f\u56f3\u3092\u4f5c\u3089\u306a\u3044\u3068\u89e3\u304f\u306e\u304c\u96e3\u3057\u3044\u305f\u3081\u3001\u5fc5\u305a\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\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\/dkdh2.jpg\" alt=\"\" width=\"328\" height=\"385\" class=\"aligncenter size-full wp-image-11843\" \/><\/p>\n<p>\u6b63\u56db\u9762\u4f53\u3067\u3042\u308b\u305f\u3081\u3001\u4e09\u89d2\u5f62\u306e\u89d2\u5ea6\u306f\u3059\u3079\u306660\u00b0\u3067\u3059\u3002\u307e\u305f\u3001\u4e09\u89d2\u5f62\u306e\u8fba\u306e\u9577\u3055\u306f\u3059\u3079\u30661\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u5185\u5206\u70b9\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\\(\\overrightarrow{OD}\\)\\(=\\displaystyle\\frac{3\\overrightarrow{b}+\\overrightarrow{c}}{1+3}\\)\\(=\\displaystyle\\frac{3\\overrightarrow{b}+\\overrightarrow{c}}{4}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{OA}\u00b7\\overrightarrow{OD}\\)<\/p>\n<p>\\(=\\overrightarrow{a}\u00b7\\left(\\displaystyle\\frac{3\\overrightarrow{b}+\\overrightarrow{c}}{4}\\right)\\)<\/p>\n<p>\\(=\\displaystyle\\frac{3}{4}\\overrightarrow{a}\u00b7\\overrightarrow{b}+\\displaystyle\\frac{1}{4}\\overrightarrow{a}\u00b7\\overrightarrow{c}\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}\\)\u3068\\(\\overrightarrow{a}\u00b7\\overrightarrow{c}\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4e09\u89d2\u5f62\u306e\u89d2\u5ea6\u306f\u3059\u3079\u306660\u00b0\u3067\u3042\u308a\u3001\u8fba\u306e\u9577\u3055\u306f\u3059\u3079\u30661\u306a\u306e\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}=1\u00d71\u00d7cos60\u00b0=\\displaystyle\\frac{1}{2}\\)<\/li>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{c}=1\u00d71\u00d7cos60\u00b0=\\displaystyle\\frac{1}{2}\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{3}{4}\\overrightarrow{a}\u00b7\\overrightarrow{b}+\\displaystyle\\frac{1}{4}\\overrightarrow{a}\u00b7\\overrightarrow{c}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{3}{4}\u00d7\\displaystyle\\frac{1}{2}+\\displaystyle\\frac{1}{4}\u00d7\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3001\\(z\\)\u6210\u5206\u3092\u5229\u7528\u3059\u308b\u5185\u7a4d\u306e\u51fa\u3057\u65b9<\/h3>\n<p>\u306a\u304a\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u3082\u3046\u4e00\u3064\u3042\u308a\u307e\u3059\u3002\u89d2\u5ea6\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3001\\(z\\)\u6210\u5206\u3092\u5229\u7528\u3057\u3066\u5185\u7a4d\u3092\u5f97\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\\(\\overrightarrow{a}=(a_1,a_2)\\)\u3001\\(\\overrightarrow{b}=(b_1,b_2)\\)\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5185\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u3068\u3059\u3067\u306b\u5b66\u3093\u3067\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}=a_1b_1+a_2b_2\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u3082\u3001\u540c\u3058\u65b9\u6cd5\u3067\u5185\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\\(\\overrightarrow{a}=(a_1,a_2,a_3)\\)\u3001\\(\\overrightarrow{b}=(b_1,b_2,b_3)\\)\u306e\u3068\u304d\u3001\u5185\u7a4d\u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{b}=a_1b_1+a_2b_2+a_3b_3\\)<\/li>\n<\/ul>\n<p><span style=\"color: #ff0000;\">\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\\(z\\)\u6210\u5206\u304c\u5897\u3048\u308b\u305f\u3081\u3001\\(a_3b_3\\)\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/span>\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u5185\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u516c\u5f0f\u306f\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u307b\u307c\u540c\u3058\u3067\u3059\u3002<\/p>\n<h2>2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2\u3092\u5229\u7528\u3057\u3001\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u51fa\u984c\u3055\u308c\u308b\u554f\u984c\u306e\u4e00\u3064\u306b\u9762\u7a4d\u306e\u8a08\u7b97\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u3067\u306f\u3001\\(a\\)\u306bsin\u03b8\u3092\u304b\u3051\u308b\u3053\u3068\u3067\u305f\u3066\u306e\u9577\u3055\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/ijhg2.jpg\" alt=\"\" width=\"600\" height=\"168\" class=\"aligncenter size-full wp-image-4829\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\\(S\\)\u3092\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/ijhg1.jpg\" alt=\"\" width=\"553\" height=\"257\" class=\"aligncenter size-full wp-image-4828\" \/><\/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>A\\((1,2,3)\\)\u3001B\\((-1,0,3)\\)\u3001C\\((1,2,-3)\\)\u3092\u9802\u70b9\u3068\u3059\u308b\u4e09\u89d2\u5f62\u306b\u3064\u3044\u3066\u3001\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3042\u3063\u3066\u3082\u3001\u4e09\u89d2\u5f62\u3067\u3042\u308c\u3070\u8fba\u306e\u9577\u3055\u3068\u89d2\u5ea6\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\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\/dkdh3.jpg\" alt=\"\" width=\"469\" height=\"274\" class=\"aligncenter size-full wp-image-11847\" \/><\/p>\n<p>\u307e\u305a\u3001\\(\\overrightarrow{AB}\\)\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(|\\overrightarrow{AB}|=\\)\\(\\sqrt{(-1-1)^2+(0-2)^2+(3-3)^2}\\)<\/p>\n<p>\\(|\\overrightarrow{AB}|=\\sqrt{8}\\)<\/p>\n<p>\\(|\\overrightarrow{AB}|=2\\sqrt{2}\\)<\/p>\n<p>\u6b21\u306b\u3001\\(\\overrightarrow{AC}\\)\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(|\\overrightarrow{AC}|=\\)\\(\\sqrt{(1-1)^2+(2-2)^2+(-3-3)^2}\\)<\/p>\n<p>\\(|\\overrightarrow{AC}|=\\sqrt{36}\\)<\/p>\n<p>\\(|\\overrightarrow{AC}|=6\\)<\/p>\n<p>\u8fba\u306e\u9577\u3055\u304c\u308f\u304b\u3063\u305f\u305f\u3081\u3001sin\u03b8\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5229\u7528\u3057\u3066sin\u03b8\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\\(|\\overrightarrow{AB}|=(-2,-2,0)\\)\u3001\\(|\\overrightarrow{AC}|=(0,0,-6)\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\\overrightarrow{AB}\u00b7\\overrightarrow{AC}\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{AB}\u00b7\\overrightarrow{AC}=-2\u00d70+(-2)\u00d70\\)\\(+0\u00d7(-6)\\)<\/p>\n<p>\\(\\overrightarrow{AB}\u00b7\\overrightarrow{AC}=0\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\overrightarrow{AB}\u00b7\\overrightarrow{AC}=|\\overrightarrow{AB}||\\overrightarrow{AC}|cos\u03b8\\)<\/p>\n<p>\\(0=2\\sqrt{2}\u00d76\u00d7cos\u03b8\\)<\/p>\n<p>\\(cos\u03b8=0\\)<\/p>\n<p>\\(cos\u03b8=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(sin\u03b8=1\\)\u3067\u3059\u3002\\(sin^2\u03b8+cos^2\u03b8=1\\)\u3060\u304b\u3089\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\\(S\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}\u00d72\\sqrt{2}\u00d76\u00d7sin\u03b8\\)<\/p>\n<p>\\(S=6\\sqrt{2}\\)<\/p>\n<p>\u306a\u304a\u6559\u79d1\u66f8\u306b\u3088\u3063\u3066\u306f\u3001\u300c\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u3066\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092\u5f97\u308b\u516c\u5f0f\u300d\u3092\u8a18\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u304c\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(S=\\displaystyle\\frac{1}{2}\\sqrt{|\\overrightarrow{a}|^2|\\overrightarrow{b}|^2-(\\overrightarrow{a}\u00b7\\overrightarrow{b})^2}\\)<\/li>\n<\/ul>\n<p>\u305f\u3060\u3001\u3053\u306e\u516c\u5f0f\u3092\u899a\u3048\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u305d\u3046\u3067\u306f\u306a\u304f\u3001\u5185\u7a4d\u3084\u8fba\u306e\u9577\u3055\u3001sin\u03b8\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u3001\u516c\u5f0f\u3092\u899a\u3048\u308b\u3053\u3068\u306a\u304f\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u306e\u5834\u5408\u3001\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308b<\/h3>\n<p>\u306a\u304a\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u308b\u6027\u8cea\u3068\u3057\u3066\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5782\u76f4\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u30022\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u306e\u5834\u5408\u3001\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5148\u307b\u3069\u306e\u9762\u7a4d\u306e\u8a08\u7b97\u3067\u306f\u3001\\(\\overrightarrow{AB}\u00b7\\overrightarrow{AC}=0\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5782\u76f4\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u5782\u76f4\u3060\u3068\\(\u03b8=90\u00b0\\)\u3001\u3064\u307e\u308a\\(cos\u03b8=0\\)\u3068\u306a\u308b\u305f\u3081\u3001\u5185\u7a4d\u306f\u5fc5\u305a\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}=(2,1,3)\\)\u3001\\(\\overrightarrow{b}=(1,-1,0)\\)\u306e\u4e21\u65b9\u306b\u5782\u76f4\u306a\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{e}\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\\(\\overrightarrow{e}=(x,y,z)\\)\u3068\u3057\u307e\u3059\u3002\\(\\overrightarrow{e}\\)\u306f\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x^2+y^2+z^2=1\\)<\/li>\n<\/ul>\n<p>\u307e\u305f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u5782\u76f4\u306e\u95a2\u4fc2\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{a}\u00b7\\overrightarrow{e}=2x+y+3z=0\\)<\/li>\n<li>\\(\\overrightarrow{b}\u00b7\\overrightarrow{e}=x-y=0\\)<\/li>\n<\/ul>\n<p>\\(x-y=0\\)\u3088\u308a\u3001\\(x=y\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(2x+y+3z=0\\)<\/p>\n<p>\\(2x+x+3z=0\\)<\/p>\n<p>\\(3x=-3z\\)<\/p>\n<p>\\(z=-x\\)<\/p>\n<p>\u6b21\u306b\u3001\\(x^2+y^2+z^2=0\\)\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x^2+y^2+z^2=1\\)<\/p>\n<p>\\(x^2+x^2+(-x)^2=1\\)<\/p>\n<p>\\(x^2=\\displaystyle\\frac{1}{3}\\)<\/p>\n<p>\\(x=\u00b1\\displaystyle\\frac{1}{3}\\)<\/p>\n<p>\\(x=\u00b1\\displaystyle\\frac{1}{\\sqrt{3}}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e2\u3064\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{e}=\\displaystyle\\frac{1}{\\sqrt{3}},\\displaystyle\\frac{1}{\\sqrt{3}},-\\displaystyle\\frac{1}{\\sqrt{3}}\\)<\/li>\n<li>\\(\\overrightarrow{e}=-\\displaystyle\\frac{1}{\\sqrt{3}},-\\displaystyle\\frac{1}{\\sqrt{3}},\\displaystyle\\frac{1}{\\sqrt{3}}\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u5782\u76f4\u3068\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\\(\\overrightarrow{e}\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u5185\u7a4d\u3092\u7528\u3044\u3066\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3092\u884c\u3046<\/h2>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3093\u3067\u3044\u308b\u5834\u5408\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u306e\u8a08\u7b97\u3092\u884c\u3046\u306e\u306f\u7c21\u5358\u3067\u3059\u3002\u5229\u7528\u3059\u308b\u516c\u5f0f\u306f\u307b\u307c\u540c\u3058\u3067\u3042\u308a\u3001\u8a08\u7b97\u65b9\u6cd5\u3082\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u7acb\u4f53\u3067\u3042\u3063\u3066\u3082\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u89d2\u5ea6\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u3067\u3059\u3002\u307e\u305f\u4e09\u89d2\u5f62\u306b\u95a2\u3059\u308b\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3067\u3042\u3063\u3066\u3082\u3001\u7acb\u4f53\u56f3\u5f62\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8fba\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u305f\u308a\u3001\u89d2\u5ea6\u3092\u5f97\u305f\u308a\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a2\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\u3053\u306e\u6027\u8cea\u306f\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u5fc5\u305a\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u3082\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u3082\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u8a08\u7b97\u65b9\u6cd5\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u65b0\u305f\u306a\u5185\u5bb9\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306e\u8a08\u7b97\u3068\u540c\u69d8\u3067\u3059\u3002 \u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3068\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u6982\u5ff5\u306f\u540c\u3058\u3067\u3059\u3002\u516c\u5f0f\u3082\u307b\u307c\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u3067\u5185\u7a4d\u3092\u7406\u89e3\u3057\u3066\u3044\u308b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11848,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11836","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\/11836","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=11836"}],"version-history":[{"count":12,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11836\/revisions"}],"predecessor-version":[{"id":11945,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11836\/revisions\/11945"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11848"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}