{"id":14748,"date":"2025-12-24T17:22:58","date_gmt":"2025-12-24T08:22:58","guid":{"rendered":"https:\/\/math-travel.com\/?p=14748"},"modified":"2026-03-06T01:11:55","modified_gmt":"2026-03-05T16:11:55","slug":"vector-equation","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-b\/vector-equation\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u6c42\u3081\u65b9\u307e\u3068\u3081\uff1a\u76f4\u7dda\u30fb\u5186\u30fb\u5e73\u9762\u306e\u516c\u5f0f\u3092\u30a4\u30e1\u30fc\u30b8\u3067\u7406\u89e3\u3059\u308b"},"content":{"rendered":"\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u4eca\u56de\u89e3\u6c7a\u3059\u308b\u60a9\u307f<\/span><\/div><div class=\"cap_box_content\">\n<p>\u300c\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3063\u3066\u306a\u306b\uff1f\u300d<br>\u300c\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3069\u3046\u4f7f\u3046\u306e\uff1f\u300d<\/p>\n<\/div><\/div>\n\n\n\n<p>\u4eca\u56de\u306f\u6570\u5b66B\u306e\u30d9\u30af\u30c8\u30eb\u304b\u3089<span class=\"huto\">\u300c\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300d<\/span>\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u5f0f\u3067\u76f4\u7dda\u3084\u5186\u306e\u6982\u5f62\u3092\u793a\u3059\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/span><\/div><div class=\"cap_box_content\">\n<p>\u2460\u3042\u308b\u70b9a\u3092\u901a\u308b\u76f4\u7dda<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"264\" height=\"201\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E7%9B%B4%E7%B7%9A%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019720566.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\"><\/p>\n\n\n\n<p>\u70b9A\u3092\u901a\u308a\u3001\u50be\u304d\u304c\\(\\vec{d}\uff08\\vec{d}\\neq0\uff09\\)\u306b\u5e73\u884c\u306a\u3001\u76f4\u7dda\\(l\\)\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+t\\vec{d} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u2461\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u76f4\u7dda<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"333\" height=\"269\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E7%95%B0%E3%81%AA%E3%82%8B2%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019796865.jpg\" alt=\"\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\"><\/p>\n\n\n\n<p>2\u3064\u306e\u70b9\u3001A,B\u3092\u901a\u308b\u76f4\u7ddal\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=(1-t)\\vec{OA}+t\\vec{OB} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u2462\u4e2d\u5fc3\\(a\\),\u534a\u5f84\\(r\\)\u306e\u5186<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"294\" height=\"242\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020336421.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\"><\/p>\n\n\n\n<p>\u70b9A\u3092\u4e2d\u5fc3\u3068\u3057\u3001\u534a\u5f84r\u306e\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>|\\vec{AP}|&amp;=&amp;r\\\\<br>\\Leftrightarrow |\\vec{OP}-\\vec{OA}|&amp;=&amp;r<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u2463\u7dda\u5206\\(AB\\)\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"222\" height=\"222\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A1.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2461\"><\/p>\n\n\n\n<p>\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\vec{AP} \\cdot \\vec{BP}&amp;=&amp;0\\\\<br>\\vec{OP}-\\vec{OA}) \\cdot (\\vec{OP}-\\vec{OB})&amp;=&amp;0<br>\\end{eqnarray}<br>\u2464\u5e73\u9762ABC<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"257\" height=\"187\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020569206.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\"><\/p>\n\n\n\n<p>\u5e73\u9762ABC\u4e0a\u306e\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC} (s,t\u306f\u5b9f\u6570)\\]<\/p>\n<\/div><\/div>\n\n\n\n<p>\u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066\u3001\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u3001\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u8868\u3059\u30d9\u30af\u30c8\u30eb\u306f\u305d\u308c\u305e\u308c\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u305f\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\uff01<\/p>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u306b\u82e6\u624b\u610f\u8b58\u304c\u3042\u308b\u65b9\u306f\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"vector\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u306f\uff1f<\/h2>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u306f<span class=\"yellow-hoso\">\u300c\u3042\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059\u70b9\u3092\u3001\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u3066\u8868\u73fe\u3057\u305f\u5f0f\u300d<\/span>\u306e\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u5f0f\u306f\u76f4\u7dda\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E7%9B%B4%E7%B7%9A%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019720566.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14757\"\/><\/figure>\n<\/div>\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+t\\vec{d} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u3092\u4e0a\u624b\u304f\u4f7f\u3044\u3001\u76f4\u7dda\u3084\u5186\u3001\u5e73\u9762\u30921\u3064\u306e\u5f0f\u3067\u8868\u3057\u305f\u3082\u306e\u304c\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"koushiki\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u4e00\u89a7<\/h2>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u306f\u300c\u76f4\u7dda\u300d\u300c\u5186\u300d\u300c\u5e73\u9762\u300d\u3092\u8868\u3059\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u8a73\u3057\u304f\u306f\u672c\u8a18\u4e8b\u306e\u5f8c\u534a\u3067\u89e3\u8aac\u3057\u307e\u3059\u304c\u3001\u307e\u305a\u306f\u30b5\u30af\u30c3\u3068\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f<\/span><\/div><div class=\"cap_box_content\">\n<ul class=\"wp-block-list\">\n<li><a href=\"#line-vector\">\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/a><\/li>\n\n\n\n<li><a href=\"#circle-vector\">\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/a><\/li>\n\n\n\n<li><a href=\"#flat-vector\">\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/a><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"line\">\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n\n\n\n<p>\u307e\u305a\u306f\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u306f2\u30d1\u30bf\u30fc\u30f3\u3042\u308a\u307e\u3059\u306e\u3067\u4f7f\u3044\u5206\u3051\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2460\u3042\u308b\u70b9\u3092\u901a\u308b\u5834\u5408<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E7%9B%B4%E7%B7%9A%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019720566.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14757\"\/><\/figure>\n<\/div>\n\n\n<p>\u70b9A\u3092\u901a\u308a\u3001\u50be\u304d\u304c\\(\\vec{d}\uff08\\vec{d}\\neq0\uff09\\)\u306b\u5e73\u884c\u306a\u3001\u76f4\u7dda\\(l\\)\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=\\vec{OA}+t\\vec{d} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2461\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u5834\u5408<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E7%95%B0%E3%81%AA%E3%82%8B2%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019796865.jpg\" alt=\"\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14760\"\/><\/figure>\n<\/div>\n\n\n<p>2\u3064\u306e\u70b9\u3001A,B\u3092\u901a\u308b\u76f4\u7ddal\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=(1-t)\\vec{OA}+t\\vec{OB} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"circle\">\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n\n\n\n<p>\u6b21\u306f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3061\u3089\u30822\u30d1\u30bf\u30fc\u30f3\u3042\u308a\u307e\u3059\u306e\u3067\u3001\u307e\u305a\u306f\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2460\u4e2d\u5fc3a,\u534a\u5f84r\u306e\u5834\u5408<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020336421.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\" class=\"wp-image-14761\"\/><\/figure>\n<\/div>\n\n\n<p>\u70b9A\u3092\u4e2d\u5fc3\u3068\u3057\u3001\u534a\u5f84r\u306e\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\begin{eqnarray}<br>|\\vec{AP}|&amp;=&amp;r\\\\<br>\\Leftrightarrow |\\vec{OP}-\\vec{OA}|&amp;=&amp;r<br>\\end{eqnarray}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2461\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5834\u5408<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A1.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2461\" class=\"wp-image-14762\"\/><\/figure>\n<\/div>\n\n\n<p>\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<div class=\"wp-block-group is-style-bg_stripe\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\\begin{eqnarray}<br>\\vec{AP} \\cdot \\vec{BP}&amp;=&amp;0\\\\<br>\\vec{OP}-\\vec{OA}) \\cdot (\\vec{OP}-\\vec{OB})&amp;=&amp;0<br>\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"flat\">\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020569206.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\" class=\"wp-image-14764\"\/><\/figure>\n<\/div>\n\n\n<p>\u5e73\u9762ABC\u4e0a\u306e\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC} (s,t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"line-vector\">\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h2>\n\n\n\n<p>\u3053\u306e\u7ae0\u3067\u306f\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3088\u308a\u8a73\u3057\u304f\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u56f3\u3092\u7528\u3044\u306a\u304c\u3089\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3057\u3066\u3044\u304f\u306e\u3067\u3001\u4e00\u7dd2\u306b\u9811\u5f35\u308a\u307e\u3057\u3087\u3046\uff01<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u3042\u308b\u70b9a\u3092\u901a\u308b\u5834\u5408<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E7%9B%B4%E7%B7%9A%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019720566.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14757\"\/><\/figure>\n<\/div>\n\n\n<p>\u70b9A\u3092\u901a\u308a\u3001\u50be\u304d\u304c\\(\\vec{d}\uff08\\vec{d}\\neq0\uff09\\)\u306b\u5e73\u884c\u306a\u3001\u76f4\u7dda\\(l\\)\u4e0a\u306e\u70b9P\u306f<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=\\vec{OA}+t\\vec{d} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u5c11\u3057\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\\(\\vec{OP}\\)\u3067\u3059\u304c\u3001\u30d9\u30af\u30c8\u30eb\u306e\u6027\u8cea\u304b\u3089\u3001\\(\\vec{OP}=\\vec{OA}+\\vec{AP}\\)\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700022117188.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14756\"\/><\/figure>\n<\/div>\n\n\n<p>\u3053\u306e\u3068\u304d\u3001\\(\\vec{AP}\\)\u3068\\(\\vec{d}\\)\u306f\u5e73\u884c\u3067\u3042\u308b\u305f\u3081\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5e73\u884c\u6761\u4ef6\u304b\u3089<br>\\(\\vec{AP}=t\\vec{d}\\)(t\u306f\u5b9f\u6570)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u5148\u307b\u3069\u306e\u5f0f\u3001\\(\\vec{OP}=\\vec{OA}+\\vec{AP}\\)\u306b\u3001\u3053\u306e\\(\\vec{AP}=t\\vec{d}\\)\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+t\\vec{d}\\]<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u3042\u308b\u70b9\u306b\u5bfe\u3057\u3066\u3001\u30d9\u30af\u30c8\u30eb\u3092\u300c\u50be\u304d\u300d\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u3067\u5f0f\u304c\u6c7a\u5b9a\u3055\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u306d\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F.jpg\" alt=\"\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14758\"\/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">\u7570\u306a\u308b2\u70b9a,b\u3092\u901a\u308b\u5834\u5408<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E7%95%B0%E3%81%AA%E3%82%8B2%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019796865.jpg\" alt=\"\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\" class=\"wp-image-14760\"\/><\/figure>\n<\/div>\n\n\n<p>2\u3064\u306e\u70b9\u3001A,B\u3092\u901a\u308b\u76f4\u7dda\\(l\\)\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=(1-t)\\vec{OA}+t\\vec{OB} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u3061\u3089\u3082\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u56f3\u3092\u898b\u308b\u3068\u5206\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u304c\u3001\\(\\vec{OP}=\\vec{OA}+t\\vec{AB}\\)\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\(\\vec{AB}=\\vec{OB}-\\vec{OA}\\)\u3067\u3042\u308b\u304b\u3089\u3001\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\vec{OP}&amp;=&amp;\\vec{OA}+t\\vec{AB}\\\\<br>\\vec{OP}&amp;=&amp;\\vec{OA}+t(\\vec{OB}-\\vec{OA})\\\\<br>\\vec{OP}&amp;=&amp;(1-t)\\vec{OA}+t\\vec{OB}<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"circle-vector\">\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h2>\n\n\n\n<p>\u6b21\u306f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3061\u3089\u3082\u4e01\u5be7\u306b\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u306d\uff01<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e2d\u5fc3a,\u534a\u5f84r\u306e\u5834\u5408<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020336421.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\" class=\"wp-image-14761\"\/><\/figure>\n<\/div>\n\n\n<p>\u70b9A\u3092\u4e2d\u5fc3\u3068\u3057\u3001\u534a\u5f84r\u306e\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306b\u5bfe\u3057\u3066\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\begin{eqnarray}<br>|\\vec{AP}|&amp;=&amp;r\\\\<br>\\Leftrightarrow |\\vec{OP}-\\vec{OA}|&amp;=&amp;r<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u56f3\u3092\u898b\u308b\u3068\u5206\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u304c\u3001\\(|\\vec{AP}|\\)\u306f\u534a\u5f84\\(r\\)\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3068\u3001\\(|\\vec{AP}|=|\\vec{OP}-\\vec{OA}|\\)\u3088\u308a\u3001\u4e0a\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3055\u3089\u306b\u3001\u5186\u306e\u65b9\u7a0b\u5f0f\u3068\u306e\u95a2\u9023\u304c\u5206\u304b\u308b\u3088\u3046\u306b\u6210\u5206\u8868\u793a\u3067\u3053\u306e\u5f0f\u3092\u8868\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\\(\\vec{OP}=(x,y),\\vec{OA}=(a_{1,}a_{2})\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\(\\vec{OP}-\\vec{OA}=(x-a_{1,}y-a_{2})\\)\u3068\u306a\u308a\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>{|\\vec{OP}-\\vec{OA}|}^{2}&amp;=&amp;r^{2}\\\\<br>{(x-a_{1})}^{2}+{(y-a_{2})}^{2}&amp;=&amp;r^{2}<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u3053\u3046\u898b\u308b\u3068\u3001\u4e2d\u5fc3\u3068\u534a\u5f84\u304c\u4e0e\u3048\u3089\u308c\u305f\u5186\u306e\u65b9\u7a0b\u5f0f\u3068\u306e\u95a2\u9023\u6027\u304c\u898b\u3048\u307e\u3059\u306d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5834\u5408<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A1.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2461\" class=\"wp-image-14762\"\/><\/figure>\n<\/div>\n\n\n<p>\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[(\\vec{OP}-\\vec{OA})\\cdot(\\vec{OP}-\\vec{OB})=0\\]<\/p>\n\n\n\n<p>\u5186\u5468\u4e0a\u306e\u70b9\u3068\u76f4\u5f84\u306e\u95a2\u4fc2\u304b\u3089\u3001\\(AP\\bot BP\\)\u3068\u306a\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A2.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2462\" class=\"wp-image-14763\"\/><\/figure>\n<\/div>\n\n\n<p>\u3053\u3053\u3067\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5782\u76f4\u6761\u4ef6\u304b\u3089\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\vec{AP}\\cdot\\vec{BP}&amp;=&amp;0\\\\<br>\\Leftrightarrow (\\vec{OP}-\\vec{OA})\\cdot(\\vec{OP}-\\vec{OB})&amp;=&amp;0<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"flat-vector\">\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020569206.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\" class=\"wp-image-14764\"\/><\/figure>\n<\/div>\n\n\n<p>\u5e73\u9762ABC\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p class=\"is-style-bg_stripe\">\\[\\vec{OP}=(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC} (s,t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\\(\\vec{OA},\\vec{OB},\\vec{OC}\\)\u306e\u4fc2\u6570\u306e\u548c\u304c1\u306b\u306a\u308b\u3053\u3068\u304c\u30dd\u30a4\u30f3\u30c8\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3061\u3089\u3082\u56f3\u3092\u7528\u3044\u306a\u304c\u3089\u8aac\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A1-e1700026272657.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2461\" class=\"wp-image-14753\"\/><\/figure>\n<\/div>\n\n\n<p>\u307e\u305a\u3001\\(\\vec{OP}=\\vec{OA}+\\vec{AP}\\)\u3068\u8868\u305b\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\\(\\vec{AP}\\)\u3067\u3059\u304c\u3001\u70b9P\u304c\u5e73\u9762ABC\u4e0a\u306b\u3042\u308b\u306e\u3067\u3001\u540c\u3058\u5e73\u9762ABC\u4e0a\u306b\u3042\u308b2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u548c\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A2-e1700026319763.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2462\" class=\"wp-image-14754\"\/><\/figure>\n<\/div>\n\n\n<p>\u5e73\u9762ABC\u4e0a\u306b\u3042\u308b\u3001\\(\\vec{AB},\\vec{AC}\\)\u3092\u4f7f\u3063\u3066\u3001<\/p>\n\n\n\n<p>\\[\\vec{AP}=s\\vec{AB}+t\\vec{AC}\uff08s,t\u306f\u5b9f\u6570\uff09\\]<\/p>\n\n\n\n<p>\u3068\u8868\u305b\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3092\u5148\u307b\u3069\u306e\\(\\vec{OP}\\)\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+s\\vec{AB}+t\\vec{AC}\uff08s,t\u306f\u5b9f\u6570\uff09\\]<\/p>\n\n\n\n<p>\u3053\u3053\u304b\u3089\u3082\u3046\u5c11\u3057\u5909\u5f62\u3057\u3066\u3001<\/p>\n\n\n\n<p>\\(\\vec{AB},\\vec{AC}\\)\u3092\\(\\vec{OA},\\vec{OB},\\vec{OC}\\)\u3092\u4f7f\u3063\u3066\u8868\u3059\u3068\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\vec{OP}&amp;=&amp;\\vec{OA}+s\\vec{AB}+t\\vec{AC}\uff08s,t\u306f\u5b9f\u6570\uff09\\\\<br>\\vec{OP}&amp;=&amp;\\vec{OA}+s(\\vec{OB}\uff0d\\vec{OA})+t(\\vec{OC}-\\vec{OA})\\\\<br>\\vec{OP}&amp;=&amp;(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC}<br>\\end{eqnarray}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"mondai\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n<p>\u76f4\u7dda\/\u5186\/\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5b66\u7fd2\u3057\u305f\u3068\u3053\u308d\u3067\u3001\u3079\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u554f\u984c\u30923\u554f\u7528\u610f\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u4eca\u307e\u3067\u5b66\u7fd2\u3057\u3066\u304d\u305f\u3053\u3068\u3092\u3082\u3068\u306b\u3001\u4e00\u7dd2\u306b\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300a\u554f\u984c\u2460\u300b<\/h3>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u7df4\u7fd2\u554f\u984c\u2460<\/span><\/div><div class=\"cap_box_content\">\n<p>\u70b9A(2,1)\u3092\u901a\u308a\u3001\\(\\vec{d}=(3,4)\\)\u306b\u5e73\u884c\u306a\u76f4\u7dda\\(l\\)\u306e\u65b9\u7a0b\u5f0f\u3092\\(x\\)\u3068\\(y\\)\u3092\u7528\u3044\u3066\u8868\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div><\/div>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u60c5\u5831\u3092\u983c\u308a\u306b\u3001\u76f4\u7dda\u306e\u5f0f\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<div class=\"swell-block-accordion\">\n<details class=\"swell-block-accordion__item\" data-swl-acc=\"wrapper\"><summary class=\"swell-block-accordion__title\" data-swl-acc=\"header\"><span class=\"swell-block-accordion__label\">\u89e3\u7b54\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b<\/span><span class=\"swell-block-accordion__icon c-switchIconBtn\" data-swl-acc=\"icon\" aria-hidden=\"true\" data-opened=\"false\"><i class=\"__icon--closed icon-caret-down\"><\/i><i class=\"__icon--opened icon-caret-up\"><\/i><\/span><\/summary><div class=\"swell-block-accordion__body\" data-swl-acc=\"body\">\n<p>\u307e\u305a\u3001\\(l\\)\u4e0a\u306e\u70b9\u3092\uff11\u3064\u53d6\u308a\u3001\u305d\u306e\u70b9\u3092\u70b9P\\((x,y)\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u3068\u304d\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+t\\vec{d}\uff08t\u306f\u5909\u6570\uff09\\]<\/p>\n\n\n\n<p>\u3068\u8868\u305b\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u304c\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u3057\u305f\u306d\uff01<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u3092\u6210\u5206\u8868\u793a\u306b\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\[(x,y)=(2,1)+t(3,4)\\]<\/p>\n\n\n\n<p>\u3088\u3063\u3066\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>x&amp;=&amp;2+3t \\cdots \u2460\\\\<br>y&amp;=&amp;1+4t \\cdots \u2461<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u2460\u2461\u3092\\(t\\)\u306b\u3064\u3044\u3066\u306e\u5f0f\u306b\u5909\u5f62\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\displaystyle t=\\frac{1}{3}x-\\frac{2}{3} \\cdots \u2462\\\\<br>\\displaystyle t=\\frac{1}{4}y-\\frac{1}{4} \\cdots \u2463<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u2462\u2463\u3088\u308a\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\displaystyle \\frac{1}{3}x-\\frac{2}{3}&amp;=&amp;\\frac{1}{4}y-\\frac{1}{4}\\\\<br>\\displaystyle y&amp;=&amp;\\frac{4}{3}x-\\frac{5}{3}<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u6c42\u3081\u308b\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\\(\\displaystyle y=\\frac{4}{3}x-\\frac{5}{3}\\)<\/p>\n<\/div><\/details>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300a\u554f\u984c\u2461\u300b<\/h3>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u7df4\u7fd2\u554f\u984c\u2461<\/span><\/div><div class=\"cap_box_content\">\n<p>\u5186\u306e\u4e2d\u5fc3\u304cA\u3067\u3001\u539f\u70b9O\u3092\u901a\u308b\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div><\/div>\n\n\n\n<p>\u6b21\u306f\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<div class=\"swell-block-accordion\">\n<details class=\"swell-block-accordion__item\" data-swl-acc=\"wrapper\"><summary class=\"swell-block-accordion__title\" data-swl-acc=\"header\"><span class=\"swell-block-accordion__label\">\u89e3\u7b54\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b<\/span><span class=\"swell-block-accordion__icon c-switchIconBtn\" data-swl-acc=\"icon\" aria-hidden=\"true\" data-opened=\"false\"><i class=\"__icon--closed icon-caret-down\"><\/i><i class=\"__icon--opened icon-caret-up\"><\/i><\/span><\/summary><div class=\"swell-block-accordion__body\" data-swl-acc=\"body\">\n<p>\u307e\u305a\u3001\u60c5\u5831\u3092\u6574\u7406\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e2d\u5fc3\u304cA\u3067\u539f\u70b9O\u3092\u901a\u308b\u5186\u306f\u4ee5\u4e0b\u306e\u56f3\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E3%81%AE%E7%B7%B4%E7%BF%92%E5%95%8F%E9%A1%8C-e1700027514930.jpg\" alt=\"\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u7df4\u7fd2\u554f\u984c\" class=\"wp-image-14755\"\/><\/figure>\n<\/div>\n\n\n<p>\u3053\u306e\u3068\u304d\u3001\u534a\u5f84\\(r\\)\u306f\\(r=AO=|\\vec{AO}|=|\\vec{OA}|\\)\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001\\(|\\vec{OP}-\\vec{OA}|=r\\)\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u304b\u3089\u3001<\/p>\n\n\n\n<p>\\[|\\vec{OP}-\\vec{OA}|=|\\vec{OA}|\\]<\/p>\n<\/div><\/details>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300a\u554f\u984c\u2462\u300b<\/h3>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u7df4\u7fd2\u554f\u984c\u2462<\/span><\/div><div class=\"cap_box_content\">\n<p>3\u70b9\\(A(4,1,3),B(-1,0,1),C(2,1,0)\\)\u304c\u5b9a\u3081\u308b\u5e73\u9762ABC\u4e0a\u306b\u70b9P\u304c\u3042\u308a\u3001\\(P(2,3,p)\\)\u3067\u3042\u308b\u3002<br>\u3053\u306e\u3068\u304d\u3001\\(p\\)\u306e\u5024\u3092\u6c42\u3081\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div><\/div>\n\n\n\n<p>\u6b21\u306f\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u3001\u70b9P\u306e\u5ea7\u6a19\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-accordion\">\n<details class=\"swell-block-accordion__item\" data-swl-acc=\"wrapper\"><summary class=\"swell-block-accordion__title\" data-swl-acc=\"header\"><span class=\"swell-block-accordion__label\">\u89e3\u7b54\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b<\/span><span class=\"swell-block-accordion__icon c-switchIconBtn\" data-swl-acc=\"icon\" aria-hidden=\"true\" data-opened=\"false\"><i class=\"__icon--closed icon-caret-down\"><\/i><i class=\"__icon--opened icon-caret-up\"><\/i><\/span><\/summary><div class=\"swell-block-accordion__body\" data-swl-acc=\"body\">\n<p>\u5e73\u9762\u4e0a\u306b\u3042\u308b\u70b9\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001\u5b9f\u6570\\(s,t\\)\u3092\u4f7f\u3063\u3066\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC}\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u305f\u3002<\/p>\n\n\n\n<p>\u4e0e\u3048\u3089\u308c\u305f\u6761\u4ef6\u304b\u3089\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>2&amp;=&amp;(1-s-t)4+s(-1)+2t\\\\<br>3&amp;=&amp;(1-s-t)1+t\\\\<br>p&amp;=&amp;(1-s-t)3+s<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u3088\u3063\u3066\u3001\u3053\u308c\u3092\u6574\u7406\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>\\(s=-2,t=6,\\)\\(p=-11\\)<\/p>\n<\/div><\/details>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"matome\">\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u4eca\u56de\u306f\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u306b\u3064\u3044\u3066\u5b66\u7fd2\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u3092\u4e0a\u624b\u304f\u4f7f\u3046\u3053\u3068\u3067\u76f4\u7dda\/\u5186\/\u5e73\u9762\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/span><\/div><div class=\"cap_box_content\">\n<p>\u2460\u3042\u308b\u70b9a\u3092\u901a\u308b\u76f4\u7dda<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"264\" height=\"201\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E3%81%82%E3%82%8B%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E7%9B%B4%E7%B7%9A%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019720566.jpg\" alt=\"\u3042\u308b\u70b9\u3092\u901a\u308b\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\"><\/p>\n\n\n\n<p>\u70b9A\u3092\u901a\u308a\u3001\u50be\u304d\u304c\\(\\vec{d}\uff08\\vec{d}\\neq0\uff09\\)\u306b\u5e73\u884c\u306a\u3001\u76f4\u7dda\\(l\\)\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=\\vec{OA}+t\\vec{d} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u2461\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u76f4\u7dda<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"333\" height=\"269\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E7%95%B0%E3%81%AA%E3%82%8B2%E7%82%B9%E3%82%92%E9%80%9A%E3%82%8B%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F-e1700019796865.jpg\" alt=\"\u7570\u306a\u308b2\u70b9\u3092\u901a\u308b\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\"><\/p>\n\n\n\n<p>2\u3064\u306e\u70b9\u3001A,B\u3092\u901a\u308b\u76f4\u7ddal\u4e0a\u306e\u70b9P\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=(1-t)\\vec{OA}+t\\vec{OB} (t\u306f\u5b9f\u6570)\\]<\/p>\n\n\n\n<p>\u2462\u4e2d\u5fc3\\(a\\),\u534a\u5f84\\(r\\)\u306e\u5186<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"294\" height=\"242\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020336421.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\"><\/p>\n\n\n\n<p>\u70b9A\u3092\u4e2d\u5fc3\u3068\u3057\u3001\u534a\u5f84r\u306e\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>|\\vec{AP}|&amp;=&amp;r\\\\<br>\\Leftrightarrow |\\vec{OP}-\\vec{OA}|&amp;=&amp;r<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\u2463\u7dda\u5206\\(AB\\)\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"222\" height=\"222\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%86%86%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A1.jpg\" alt=\"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2461\"><\/p>\n\n\n\n<p>\u7dda\u5206AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u4e0a\u306b\u3042\u308b\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\\vec{AP} \\cdot \\vec{BP}&amp;=&amp;0\\\\<br>\\vec{OP}-\\vec{OA}) \\cdot (\\vec{OP}-\\vec{OB})&amp;=&amp;0<br>\\end{eqnarray}<br>\u2464\u5e73\u9762ABC<\/p>\n\n\n\n<p><img decoding=\"async\" width=\"257\" height=\"187\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2023\/11\/%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F%E2%91%A0-e1700020569206.jpg\" alt=\"\u5e73\u9762\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u2460\"><\/p>\n\n\n\n<p>\u5e73\u9762ABC\u4e0a\u306e\u70b9P\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>\\[\\vec{OP}=(1-s-t)\\vec{OA}+s\\vec{OB}+t\\vec{OC} (s,t\u306f\u5b9f\u6570)\\]<\/p>\n<\/div><\/div>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u306f\u3001<span class=\"hutoaka\">\u300c\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u300d<\/span>\u306b\u3064\u3044\u3066\u3082\u3057\u3063\u304b\u308a\u3068\u7406\u89e3\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u6700\u5f8c\u307e\u3067\u3054\u89a7\u3044\u305f\u3060\u304d\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u307f\u3093\u306a\u306e\u52aa\u529b\u304c\u5831\u308f\u308c\u307e\u3059\u3088\u3046\u306b\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u56de\u306f\u6570\u5b66B\u306e\u30d9\u30af\u30c8\u30eb\u304b\u3089\u300c\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u300d\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u5f0f\u3067\u76f4\u7dda\u3084\u5186\u306e\u6982\u5f62\u3092\u793a\u3059\u3082\u306e\u3067\u3059\u3002 \u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066\u3001\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u3001\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u8868\u3059\u30d9\u30af\u30c8 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":14752,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[16,225],"tags":[17,14,11],"class_list":["post-14748","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-vector","category-math-b","tag-17","tag-b","tag-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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