{"id":5305,"date":"2025-01-02T17:37:34","date_gmt":"2025-01-02T08:37:34","guid":{"rendered":"https:\/\/torisetudy.com\/?p=5305"},"modified":"2026-03-09T17:41:12","modified_gmt":"2026-03-09T08:41:12","slug":"%e5%86%85%e7%a9%8d","status":"publish","type":"post","link":"https:\/\/torisetudy.com\/?p=5305","title":{"rendered":"\u5185\u7a4d"},"content":{"rendered":"\n<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5185\u7a4d\u3068\u6210\u5206<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u5185\u7a4d\u306e\u6027\u8cea<\/a><\/li><\/ul><\/div>\n<h2 class=\"wp-block-heading\"><span id=\"i\">\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u7fa9<\/h3>\n\n\n\n<p>\u5e73\u9762\u4e0a\u306b3\u70b9 $\\rmO$\uff0c$\\rmA$\uff0c$\\rmB$ \u304c\u3042\u308a\uff0c$\\angle \\rmA\\rmO\\rmB=\\theta$\uff0c$\\vec{a}=\\vec{\\rmO\\rmA}$\uff0c$\\vec{b}=\\vec{\\rmO\\rmB}$ \u3068\u3057\u307e\u3059\u3002$\\triangle\\rmO\\rmA\\rmB$ \u306b\u3064\u3044\u3066\uff0c\u4f59\u5f26\u5b9a\u7406\u3088\u308a\uff0c<\/p>\n\n\n\n<p>$$\\begin{aligned}\\left|\\vec{\\rmA\\rmB}\\right|^2=\\left|\\vec{a}\\right|^2+\\left|\\vec{b}\\right|^2-2\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta\\stext{\\quad\u2026\\ \u2460}\\end{aligned}$$\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u304b\u3089\uff0c$\\theta$ \u306e\u5024\u306b\u3088\u3063\u3066 $\\left|\\vec{\\rmA\\rmB}\\right|$ \u306e\u5927\u304d\u3055\u306f\u5909\u5316\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u306e\u3067\uff0c$\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta$ \u3068\u3044\u3046\u5024\u306f\u4f55\u304b\u3057\u3089\u306e\u610f\u5473\u304c\u3042\u308a\u305d\u3046\u3067\u3059\u306d\u3002<\/p>\n\n\n\n<p>\u3053\u306e\uff0c$\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta$ \u3092 $\\vec{a}$ \u3068 $\\vec{b}$ \u306e<span class=\"st-mymarker-s\">\u5185\u7a4d<\/span>\u3068\u3044\u3044\uff0c<span class=\"st-mymarker-s\">$\\vec{a}\\cdot\\vec{b}$<\/span> \u3067\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u2460<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$\\vec{0}$ \u3067\u306a\u30442\u3064\u306e\u30d9\u30af\u30c8\u30eb $\\vec{a}$\uff0c$\\vec{b}$ \u306e\u306a\u3059\u89d2\u3092 $\\theta\\ (0\\Deg\\leqq\\theta\\leqq180\\Deg)$ \u3068\u3059\u308b\u3068\u304d\uff0c$\\vec{a}$\uff0c$\\vec{b}$ \u306e\u5185\u7a4d$\\vec{a}\\cdot\\vec{b}$ \u3092\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\vec{a}\\cdot\\vec{b}=\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta$$\u3068\u5b9a\u7fa9\u3059\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i-2\">\u5185\u7a4d\u3068\u6210\u5206<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5185\u7a4d\u306e\u8a08\u7b97<\/h3>\n\n\n\n<p>\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u539f\u70b9 $\\rmO$\uff0c$\\rmA(x_1,\\,y_1)$\uff0c$\\rmB(x_2,\\,y_2)$ \u3068\u5ea7\u6a19\u3092\u8a2d\u5b9a\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>$\\angle \\rmA\\rmO\\rmB=\\theta$\uff0c$\\vec{a}=\\vec{\\rmO\\rmA}$\uff0c$\\vec{b}=\\vec{\\rmO\\rmB}$ \u3068\u3059\u308b\u3068\uff0c<\/p>\n\n\n\n<p>$$\\begin{aligned} &amp;\\left|\\vec{\\rmA\\rmB}\\right|^2=(x_2-x_1)^2+(y_2-y_1)^2\\\\ &amp;\\left|\\vec{\\rmO\\rmA}\\right|^2=\\left|\\vec{a}\\right|^2=x_1^2+y_1^2\\\\&amp;\\left|\\vec{\\rmO\\rmB}\\right|^2=\\left|\\vec{b}\\right|^2=x_2^2+y_2^2 \\end{aligned}$$\u304c\u305d\u308c\u305e\u308c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon4 clearfix\"><div class=\"st-kaiwa-area2\"><div class=\"st-kaiwa-hukidashi2\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u3053\u306e\u7d50\u679c\u3092\u5229\u7528\u3057\u3066\u4f59\u5f26\u5b9a\u7406\u3092\u6574\u7406\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff01<\/p>\n<\/div><\/div><\/div><div class=\"st-kaiwa-face2\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u751f\u5f92\uff08\u5b66\u7fd2\uff09.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u751f\u5f92\uff08\u5b66\u7fd2\uff09.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name2\">\u751f\u5f92<\/div><\/div><\/div>\n\n\n\n<p>$\\triangle\\rmO\\rmA\\rmB$ \u306b\u3064\u3044\u3066\uff0c\u4f59\u5f26\u5b9a\u7406\u3088\u308a\uff0c<\/p>\n\n\n\n<p>$$\\left|\\vec{\\rmA\\rmB}\\right|^2=\\left|\\vec{a}\\right|^2+\\left|\\vec{b}\\right|^2-2\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta$$\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\uff0c\u3053\u308c\u306b\u5148\u307b\u3069\u306e3\u3064\u306e\u5f0f\u306e\u7d50\u679c\u3092\u4ee3\u5165\u3057\u3066\u6574\u7406\u3059\u308b\u3068\uff0c<\/p>\n\n\n\n<p>$$\\begin{aligned}&amp;(x_2-x_1)^2+(y_2-y_1)^2=x_1^2+y_1^2+x_2^2+y_2^2-2\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta\\\\&amp;\\therefore\\quad\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta=x_1x_2+y_1y_2 \\end{aligned}$$\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5f0f\u306e\u5de6\u8fba\u306f\uff0c$\\vec{a}\\cdot\\vec{b}$ \u3067\u3059\u304b\u3089\uff0c\u6b21\u306e\u3053\u3068\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u2461<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$\\vec{0}$ \u3067\u306a\u30442\u3064\u306e\u30d9\u30af\u30c8\u30eb $\\vec{a}=(x_1,\\,y_1)$\uff0c$\\vec{b}=(x_2,\\,y_2)$ \u306e\u5185\u7a4d\u306f\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\vec{a}\\cdot\\vec{b}=\\dbinom{x_1}{y_1}\\cdot\\dbinom{x_2}{y_2}=x_1x_2+y_1y_2$$<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u6ce8\u610f\u70b9<\/h3>\n\n\n\n<p>\u5185\u7a4d $\\vec{a}\\cdot\\vec{b}$ \u306f\uff0c\u300c$\\cdot$\u300d\u3068\u3044\u3046\u8a18\u53f7\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\u304b\u3051\u7b97\u306e\u3088\u3046\u306b\u601d\u308f\u308c\u304c\u3061\u3067\u3059\u304c\uff0c<span class=\"st-mymarker-s-b\">\u3053\u308c\u306f\u304b\u3051\u7b97\u3067\u306f\u3042\u308a\u307e\u305b\u3093<\/span>\u3002<\/p>\n\n\n\n<p>\u300c$\\cdot$\u300d\u3068\u3044\u3046\u8a18\u53f7\u304c\u300c\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u300d\u3068\u3044\u3046\u6f14\u7b97\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u307e\u305f\uff0c<span class=\"st-mymarker-s-b\">\u5185\u7a4d\u306e\u6f14\u7b97\u7d50\u679c\u306f\u30d9\u30af\u30c8\u30eb\u3067\u306f\u306a\u304f\u30b9\u30ab\u30e9\u30fc\u306b\u306a\u3063\u3066\u3044\u308b<\/span>\u3053\u3068\u3082\u30dd\u30a4\u30f3\u30c8\u3067\u3059\u30022\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304b\u3089\u751f\u307e\u308c\u308b\u65b0\u3057\u3044\u5024\uff08\u30b9\u30ab\u30e9\u30fc\uff09\u3060\u3068\u8003\u3048\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u3053\u3053\u306e\u90e8\u5206\uff0c\u3068\u3063\u3066\u3082\u5927\u4e8b\uff01<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<p>\u6ce8\u610f\u70b9\u3067\u3059\u304c\uff0c$\\vec{a}\\cdot\\vec{b}$ \u306e\u300c$\\cdot$\u300d\u8a18\u53f7\u3092\u7701\u7565\u3057\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u307e\u305f\uff0c$\\vec{a}\\times\\vec{b}$ \u306f\u5185\u7a4d\u3067\u306f\u306a\u304f\u300c\u5916\u7a4d\u300d\u3068\u3044\u3046\u5225\u306e\u6f14\u7b97\u306b\u306a\u308a\u307e\u3059\u306e\u3067\uff0c$\\vec{a}\\cdot\\vec{b}$ \u3092 $\\vec{a}\\times\\vec{b}$ \u306e\u3088\u3046\u306b\u304b\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u89d2\u5ea6\u306e\u8a08\u7b97<\/h3>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2\u3092\u5185\u7a4d\u3067\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002$\\vec{a}\\cdot\\vec{b}=\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|\\cos\\theta$ \u3088\u308a\uff0c\u6b21\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2\u3068\u5185\u7a4d<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$\\vec{0}$ \u3067\u306a\u30442\u3064\u306e\u30d9\u30af\u30c8\u30eb $\\vec{a}$\uff0c$\\vec{b}$ \u306e\u306a\u3059\u89d2 $\\theta$ \u306b\u3064\u3044\u3066\uff0c\u4ee5\u4e0b\u304c\u6210\u7acb\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\cos\\theta=\\bun{\\vec{a}\\cdot\\vec{b}}{\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|}$$<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i-3\">\u5185\u7a4d\u306e\u6027\u8cea<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u3055\u307e\u3056\u307e\u306a\u6027\u8cea<\/h3>\n\n\n\n<p>\u5ea7\u6a19\u5e73\u9762\u3067\u306e\u5b9a\u7fa9\u304b\u3089\uff0c\u5185\u7a4d\u306f\u4ee5\u4e0b\u306e\u6027\u8cea\u3092\u3082\u3064\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u5185\u7a4d\u306e\u6027\u8cea \u305d\u306e1<\/p><div class=\"st-in-mybox\">\n<p>\u4ee5\u4e0b\u306e\u95a2\u4fc2\u5f0f\u304c\u6210\u7acb\u3059\u308b\u3002<\/p>\n\n\n\n<p>$$\\begin{aligned}&amp;\\stext{\u2460}\\ \\vec{a}\\cdot\\vec{b}=\\vec{b}\\cdot\\vec{a}\\\\&amp;\\stext{\u2461}\\ \\left(\\vec{a}+\\vec{b}\\right)\\cdot\\vec{c}=\\vec{a}\\cdot\\vec{c}+\\vec{b}\\cdot\\vec{c}\\\\&amp;\\stext{\u2462}\\ \\left(k\\vec{a}\\right)\\cdot\\vec{b}=k\\vec{a}\\cdot\\vec{b}\\quad \\stext{\uff08\u305f\u3060\u3057 $k$ \u306f\u5b9a\u6570\uff09}\\\\&amp;\\stext{\u2463}\\ \\vec{a}\\cdot\\vec{a}=\\left|\\vec{a}\\right|^2\\end{aligned}$$<\/p>\n<\/div><\/div>\n\n\n\n<p>\u2460\u301c\u2462\u306b\u3064\u3044\u3066\u306f\uff0c\u5185\u7a4d\u3092\u8868\u3059\u8a18\u53f7\u3067\u3042\u308b\u300c$\\cdot$\u300d\u306f\u7701\u7565\u3067\u304d\u306a\u3044\u3082\u306e\u306e\uff0c\u6587\u5b57\u5f0f\u306e\u304b\u3051\u7b97\u3068\u540c\u3058\u3088\u3046\u306a\u30a4\u30e1\u30fc\u30b8\u3067\u3059\u306d\u3002<\/p>\n\n\n\n<p>\u2463\u306e $\\vec{a}\\cdot\\vec{a}$ \u306f\uff0c\u306a\u3059\u89d2\u304c $0\\Deg$, \u306a\u306e\u3067\uff0c<\/p>\n\n\n\n<p>$$\\vec{a}\\cdot\\vec{a}=\\left|\\vec{a}\\right|\\left|\\vec{a}\\right|\\cos0\\Deg=\\left|\\vec{a}\\right|^2$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u307e\u305f\uff0c\u3053\u306e\u6027\u8cea \u2463\u3088\u308a\uff0c\u6b21\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u5185\u7a4d\u306e\u6027\u8cea \u305d\u306e2<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u7acb\u3059\u308b\u3002<\/p>\n\n\n\n<p>$$\\left|\\vec{a}\\pm\\vec{b}\\right|^2=\\left|\\vec{a}\\right|^2\\pm2\\vec{a}\\cdot\\vec{b}+\\left|\\vec{b}\\right|^2\\quad\\stext{\uff08\u8907\u53f7\u540c\u9806\uff09}$$<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u8a3c\u660e\u3082\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<p>\u4ee5\u4e0b\uff0c\u8907\u53f7\u540c\u9806\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p>$$\\begin{aligned} \\left|\\vec{a}\\pm\\vec{b}\\right|^2&amp;=(\\vec{a}\\pm\\vec{b})\\cdot(\\vec{a}\\pm\\vec{b})\\\\ &amp;=\\vec{a}\\cdot\\vec{a}\\pm\\vec{a}\\cdot\\vec{b}\\pm\\vec{b}\\cdot\\vec{a}+\\vec{b}\\cdot\\vec{b}\\\\ &amp;=\\left|\\vec{a}\\right|^2\\pm2\\vec{a}\\cdot\\vec{b}+\\left|\\vec{b}\\right|^2 \\end{aligned}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 \u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d2 \u5185\u7a4d\u3068\u6210\u52063 \u5185\u7a4d\u306e\u6027\u8cea \u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d \u5b9a\u7fa9 \u5e73\u9762\u4e0a\u306b3\u70b9 $\\rmO$\uff0c$\\rmA$\uff0c$\\rmB$ \u304c\u3042\u308a\uff0c$\\angle \\rmA\\rmO\\rmB=\\theta$\uff0c$\\ &#8230; <\/p>\n","protected":false},"author":1,"featured_media":5328,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,32],"tags":[],"class_list":["post-5305","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-vector","category-32"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5305"}],"collection":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5305"}],"version-history":[{"count":22,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5305\/revisions"}],"predecessor-version":[{"id":5457,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5305\/revisions\/5457"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/media\/5328"}],"wp:attachment":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}