{"id":210,"date":"2023-07-11T20:48:25","date_gmt":"2023-07-11T20:48:25","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e5%85%ac%e5%bc%8f%e7%9a%84%e6%a8%a1%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-11T20:48:25","modified_gmt":"2023-07-11T20:48:25","slug":"%e5%90%91%e9%87%8f%e5%85%ac%e5%bc%8f%e7%9a%84%e6%a8%a1%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e5%85%ac%e5%bc%8f%e7%9a%84%e6%a8%a1%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u5982\u4f55\u8ba1\u7b97\u5411\u91cf\u7684\u6a21"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u770b\u5230\u77e2\u91cf\u5927\u5c0f\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u5176\u516c\u5f0f\u8ba1\u7b97\u77e2\u91cf\u5927\u5c0f\u7684\u8bf4\u660e\u3002\u60a8\u8fd8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u4ece\u4e24\u70b9\u627e\u5230\u6a21\u5757\uff1a\u5176\u8d77\u70b9\u548c\u7ec8\u70b9\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u6839\u636e\u5411\u91cf\u7684\u6a21\u548c\u5411\u91cf\u6a21\u7684\u5c5e\u6027\u6765\u786e\u5b9a\u5411\u91cf\u7684\u5206\u91cf\u3002\u60a8\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u793a\u4f8b\u3001\u7ec3\u4e60\u548c\u5206\u6b65\u95ee\u9898\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-modulo-de-un-vector\"><\/span>\u5411\u91cf\u7684\u6a21\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5411\u91cf\u7684\u5927\u5c0f<\/strong>\u8868\u793a\u5176\u539f\u70b9\u548c\u7ec8\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u56e0\u6b64\uff0c\u77e2\u91cf\u7684\u5927\u5c0f\u7b49\u4e8e\u8be5\u77e2\u91cf\u7684<strong>\u957f\u5ea6<\/strong>\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/module-dune-longueur-de-vecteur.webp\" alt=\"\u957f\u5ea6\u5411\u91cf\u7684\u6a21\" class=\"wp-image-353\" width=\"182\" height=\"179\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u6b63\u5982\u60a8\u5728\u4e0a\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\u770b\u5230\u7684\uff0c\u77e2\u91cf\u7684\u5927\u5c0f\u7531\u77e2\u91cf\u4e24\u4fa7\u7684\u5782\u76f4\u6761\u8868\u793a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7513a2086faba37053531b9addea2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{AB}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5411\u91cf\u7684\u6a21\u4e0e<strong>\u5411\u91cf\u7684\u8303\u6570<\/strong>\u76f8\u540c\uff0c\u6240\u4ee5\u4f60\u4e5f\u53ef\u4ee5\u770b\u5230\u5b83\u662f\u8fd9\u6837\u5199\u7684\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6709\u4e9b\u6570\u5b66\u5bb6\u4e5f\u7528\u6bcf\u8fb9\u4e24\u4e2a\u7ad6\u6761\u6765\u8868\u793a\u5411\u91cf\u7684\u6a21\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdcec36c9625381e65a49270cd8a2331_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\lvert \\vv{AB}\\rvert\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-modulo-de-un-vector\"><\/span>\u5411\u91cf\u6a21\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u627e\u5230\u5e73\u9762\u4e2d\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u4e3a\u4e86\u786e\u5b9a<strong>\u5411\u91cf\u7684\u5927\u5c0f\uff0c<\/strong>\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u5176\u5206\u91cf\u5e73\u65b9\u548c\u7684\uff08\u6b63\uff09\u5e73\u65b9\u6839\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u6709\u4ee5\u4e0b\u5411\u91cf\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4b2f8c9cdb09377a66fbce8392c30ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5176\u6a21\u5757\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f63fa0a6f4110553705d4e3d6cf23692_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ \\text{u}_x^2+\\text{u}_y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"117\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u5411\u91cf\u7684\u5927\u5c0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e1f083b8e9df80dc493a280f5c20cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c93cbb567f755c6f6f5ed9ddd8fce245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =\\sqrt{4^2+3^2} = \\sqrt{16+9}=\\sqrt{25} = \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"285\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-el-modulo-de-un-vector-con-las-coordenadas-de-su-origen-y-su-extremo\"><\/span>\u7528\u539f\u70b9\u548c\u7ec8\u70b9\u7684\u5750\u6807\u8ba1\u7b97\u5411\u91cf\u7684\u5927\u5c0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u5f53\u6211\u4eec\u77e5\u9053\u5411\u91cf\u7684\u5206\u91cf\u65f6\u5982\u4f55\u786e\u5b9a\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u4f46\u662f\u5982\u679c\u6211\u4eec\u53ea\u77e5\u9053\u5b83\u7684\u8d77\u70b9\u548c\u7ec8\u70b9\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u6839\u636e\u5411\u91cf\u7684\u539f\u70b9\u548c\u7ec8\u70b9\u5750\u6807\u8ba1\u7b97\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u5fc5\u987b\u9075\u5faa\u4ee5\u4e0b\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u9996\u5148\u6211\u4eec\u627e\u5230\u5411\u91cf\u7684\u5206\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u51cf\u53bb\u6781\u503c\u51cf\u53bb\u539f\u70b9\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u7528\u4e0a\u4e00\u8282\u4e2d\u770b\u5230\u7684\u516c\u5f0f\u83b7\u5f97\u7684\u5411\u91cf\u7684\u6a21\u3002<\/span><\/li>\n<\/ol>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u770b\u770b\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u8be5\u70b9\u4e3a\u539f\u70b9\u7684\u5411\u91cf\u7684\u5927\u5c0f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a16d799fdc0fa3c371c35ba5f0f3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6700\u540e\u4e00\u70b9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a3a744084783890d8d12db98e82e348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(-1,4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p>\u6211\u4eec\u9996\u5148\u9700\u8981\u627e\u5230\u5411\u91cf\u7684\u5206\u91cf\uff0c\u56e0\u6b64\u6211\u4eec\u51cf\u53bb\u5b83\u7684\u7aef\u70b9\u51cf\u53bb\u5b83\u7684\u539f\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2837e9a238c2d7143e91f36f1bdc953d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A=(-1,4)-(2,1)=(-3,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u5411\u91cf\u5e45\u5ea6\u516c\u5f0f\u8ba1\u7b97\u5176\u5e45\u5ea6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32da93798b33cfd623c145783850b8b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\vv{AB} \\end{vmatrix} =\\sqrt{(-3)^2+3^2} = \\sqrt{9+9}=\\sqrt{18}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"295\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u7ed3\u679c\u4fdd\u7559\u4e3a\u5e73\u65b9\u6839\uff0c\u56e0\u4e3a\u5b83\u4e0d\u7cbe\u786e\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-las-componentes-de-un-vector-a-partir-de-su-modulo\"><\/span>\u5982\u4f55\u6839\u636e\u5411\u91cf\u7684\u6a21\u8ba1\u7b97\u5411\u91cf\u7684\u5206\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u5982\u4f55\u4ece\u5411\u91cf\u7684\u5206\u91cf\u4e2d\u63d0\u53d6\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u4f46\u8be5\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u98a0\u5012\u8fc7\u6765\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5411\u91cf\u7684\u6a21\u6765\u8ba1\u7b97\u5411\u91cf\u7684\u5206\u91cf\u3002<\/p>\n<p>\u4ece\u5411\u91cf\u7684\u5927\u5c0f\u627e\u5230\u5411\u91cf\u5206\u91cf\u7684\u8fc7\u7a0b\u79f0\u4e3a<strong>\u5411\u91cf\u5206\u89e3<\/strong>\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u5206\u89e3\u77e2\u91cf\uff0c\u6211\u4eec\u663e\u7136\u9700\u8981\u5b83\u7684\u5927\u5c0f\uff0c\u4ee5\u53ca\u5b83\u4e0e\u6a2a\u5750\u6807\u8f74\uff08X \u8f74\uff09\u5f62\u6210\u7684\u89d2\u5ea6\u3002<\/p>\n<p>\u8fd9\u6837\u5411\u91cf\u7684 X \u548c Y \u5206\u91cf\u5c31\u53ef\u4ee5\u7528\u4e09\u89d2\u6bd4\u6765\u8ba1\u7b97\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/decomposition-dun-vecteur-dans-matab.webp\" alt=\"matlab\u4e2d\u5411\u91cf\u7684\u5206\u89e3\" class=\"wp-image-388\" width=\"390\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u5728\u56fe\u50cf\u4e2d\u770b\u5230\u7684\uff0c\u77e2\u91cf\u7684\u5927\u5c0f\u4e0e\u5176\u5206\u91cf\u5f62\u6210\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u56e0\u6b64\u53ef\u4ee5\u5e94\u7528\u4e09\u89d2\u5b66\u7684\u57fa\u672c\u516c\u5f0f\u3002<\/p>\n<p>\u5fc5\u987b\u8003\u8651\u5230\uff0c\u4e0e\u5411\u91cf\u7684\u6a21\u4e0d\u540c\uff0c\u5b83\u7684\u5206\u91cf\u53ef\u4ee5\u4e3a\u8d1f\uff0c\u56e0\u4e3a\u6b63\u5f26\u548c\u4f59\u5f26\u53ef\u4ee5\u53d6\u8d1f\u503c\u3002<\/p>\n<p>\u4f5c\u4e3a\u4e00\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u5411\u91cf\u7684\u5411\u91cf\u5206\u89e3\uff0c\u5176\u5927\u5c0f\u548c\u4e0e OX \u8f74\u7684\u89d2\u5ea6\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3899abb56397b041d612a1fb9d33a70a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert = 10 \\qquad \\alpha = 60\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u77e2\u91cf\u7684\u6c34\u5e73\u5206\u91cf\u7b49\u4e8e\u6a21\u4e58\u4ee5\u89d2\u5ea6\u7684\u4f59\u5f26\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3b237fcbcb6df7294c9b2dd5d7f06cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_x= \\lvert \\vv{\\text{u}}\\rvert \\cdot \\text{cos}(60\u00ba)= 10 \\cdot 0,5 = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5411\u91cf\u7684\u5782\u76f4\u5206\u91cf\u7b49\u4e8e\u6a21\u4e58\u4ee5\u89d2\u5ea6\u7684\u6b63\u5f26\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2f9805cff94727a43f3bf53e78e9133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_y= \\lvert \\vv{\\text{u}}\\rvert \\cdot \\text{sen}(60\u00ba)= 10 \\cdot 0,87 = 8,7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"268\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u5411\u91cf\u5982\u4e0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8137f59704bc3ee0eabf752d669ce25d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{ = (5 \\ ,\\ 8,7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-modulo-de-un-vector\"><\/span>\u5411\u91cf\u7684\u6a21\u5c5e\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6a21\u662f\u4e00\u79cd\u5411\u91cf\u8fd0\u7b97\uff0c\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\u5411\u91cf\u7684\u5927\u5c0f<strong>\u6c38\u8fdc\u4e0d\u80fd\u4e3a\u8d1f<\/strong>\uff0c\u5b83\u59cb\u7ec8\u7b49\u4e8e\u6216\u5927\u4e8e 0\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-923d73a359ab40f1ffaba643bff0ca98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert \\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u552f\u4e00\u5b58\u5728\u7684\u5e45\u5ea6\u4e3a\u96f6\u7684\u5411\u91cf\u662f\u96f6\u5411\u91cf\uff0c\u5373\u5411\u91cf<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3fbfff66ff910ebae6196cf59b4251eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (0,0) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5411\u91cf\u4e0e\u5b9e\u6570\uff08\u6216\u6807\u91cf\uff09\u4e58\u79ef\u7684\u5927\u5c0f\u76f8\u5f53\u4e8e\u6807\u91cf\u7684\u7edd\u5bf9\u503c\u4e58\u4ee5\u5411\u91cf\u7684\u5927\u5c0f\u3002\u56e0\u6b64\uff0c\u4ee5\u4e0b\u7b49\u5f0f\u6210\u7acb\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c814e6a42f23a1c1ab2c413261fa3d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert k \\cdot \\vv{\\text{u}} \\rvert = \\lvert k  \\rvert \\cdot \\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u4e09\u89d2\u4e0d\u7b49\u5f0f<\/strong>\u5f97\u5230\u9a8c\u8bc1\uff1a\u4e24\u4e2a\u5411\u91cf\u4e4b\u548c\u7684\u6a21\u5206\u522b\u5c0f\u4e8e\u6216\u7b49\u4e8e\u5b83\u4eec\u5404\u81ea\u7684\u6a21\u4e4b\u548c\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63e1eae823666827bce2c51133a8a49b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}+\\vv{\\text{v}} \\rvert \\leq \\lvert\\vv{\\text{u}} \\rvert+\\lvert\\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6b64\u5916\uff0c\u4e24\u4e2a\u5411\u91cf\u4e4b\u548c\u7684\u5927\u5c0f\u4e0e\u70b9\u79ef\u76f8\u5173\uff0c\u516c\u5f0f\u5982\u4e0b\uff1a <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a16809d6f89f2053f5c732a7acd486ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}+\\vv{\\text{v}} \\rvert = \\sqrt{\\lvert \\vv{\\text{u}} \\rvert ^2+\\lvert \\vv{\\text{v}} \\rvert ^2 +2\\cdot \\vv{\\text{u}}\\cdot \\vv{\\text{v}} \\vphantom{\\sqrt{x^2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"242\" style=\"vertical-align: -9px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"vector-unitario\"><\/span>\u5355\u4f4d\u5411\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u5355\u4f4d\u5411\u91cf<\/strong>\u662f\u6a21\u7b49\u4e8e\u4e00\u7684\u5411\u91cf\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d377140c532b698d7cdb3b180f2b7e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5355\u4f4d\u5411\u91cf\u7684\u957f\u5ea6\u662f\u4e00\u4e2a\u5355\u4f4d\u3002<\/p>\n<p>\u8ba9\u4e00\u4e2a\u5411\u91cf\u7684\u6a21\u6070\u597d\u4e3a 1 \u770b\u8d77\u6765\u975e\u5e38\u56f0\u96be\uff0c\u4f46\u5b9e\u9645\u4e0a\u5f88\u5bb9\u6613\u627e\u5230\u8fd9\u79cd\u7c7b\u578b\u7684\u5411\u91cf\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u8981\u627e\u5230\u4efb\u4f55\u5411\u91cf\u7684\u5355\u4f4d\u5411\u91cf\uff0c\u53ea\u9700\u5c06\u5176\u9664\u4ee5\u5176\u6a21\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b8ce39ff18883208f914f48d4463051_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_u = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"64\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62e58ce540d042ffd138cfec23ebac58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_u\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u5355\u4f4d\u5411\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d6a20023310ef9d6c49931c265af1ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}},\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a59cd4f2581db3318d38a2a77340a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4f60\u7684\u6a21\u5757\u3002<\/p>\n<\/div>\n<p>\u5355\u4f4d\u5411\u91cf\u4e5f\u79f0\u4e3a versor \u6216\u5f52\u4e00\u5316\u5411\u91cf\u3002<\/p>\n<p>\u53e6\u5916\uff0c\u5355\u4f4d\u5411\u91cf\u4e0e\u539f\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u548c\u65b9\u5411\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u4ee5\u4e0b\u5411\u91cf\u7684\u5355\u4f4d\u5411\u91cf\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06fc528ca9d541ea032c50af916549a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u6807\u51c6\u5316\u5411\u91cf\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u8ba1\u7b97\u5b83\u7684\u5927\u5c0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86ef7a2aa2d0201e764e4868b473b3e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert=\\sqrt{1^2+(-1)^2} = \\sqrt{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"188\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u539f\u59cb\u5411\u91cf\u9664\u4ee5\u5176\u6a21\u6765\u8ba1\u7b97\u5355\u4f4d\u5411\u91cf\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-668d60d54811f2fd2be96dd0180563ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{v}}_u = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}} \\rvert} = \\frac{(1,-1)}{\\sqrt{2}}= \\bm{\\left(\\frac{1}{\\sqrt{2}},-\\frac{1}{\\sqrt{2}} \\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"267\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-modulos-de-vectores\"><\/span>\u89e3\u51b3\u5411\u91cf\u6a21\u5757\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u5411\u91cf\u7684\u5927\u5c0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78feb0de1149c92d8000673c3bd9c750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(6,8)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u5411\u91cf\u7684\u6a21\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u5176\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2223831dac0e96dc39b2c1f575a96656_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert\\vv{a} \\rvert= \\sqrt{6^2+8^2} =\\sqrt{36+64} = \\sqrt{100} = \\bm{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u5c06\u4ee5\u4e0b\u5411\u91cf\u4ece\u6700\u77ed\u5230\u6700\u957f\u6392\u5e8f\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd5b4cce27e3e747335f1b83a27ea14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9528dc0e7c4fdec1f5ea0897cb5f1080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{b}=(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3d0c1b4ab12a00987c3821811108881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{c}=(5,12)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9611ddc072acda8752bf9cf38687c790_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{d}=(-6,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5411\u91cf\u7684\u957f\u5ea6\u7b49\u4e8e\u5176\u5927\u5c0f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6240\u6709\u5411\u91cf\u7684\u6a21\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f774b05c948e7cc2648508e840bec8d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\vv{a}\\right|= \\sqrt{4^2+(-2)^2} =\\sqrt{16+4} = \\sqrt{20}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"284\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26f7996534e539a7c403a494276e9b43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{b}|= \\sqrt{3^2+1^2} =\\sqrt{9+1} = \\sqrt{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"243\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41d80256e32169ae228c30631ed6a7c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix}\\vv{c}\\end{vmatrix}= \\sqrt{5^2+12^2} =\\sqrt{25+144} = \\sqrt{169} = 13\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"331\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8d50ea2580fbf8d44a19147ea34b730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{d}| = \\sqrt{(-6)^2+(-3)^2} =\\sqrt{36+9} = \\sqrt{45}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4ece\u6700\u5c0f\u5230\u6700\u5927\u957f\u5ea6\uff08\u6216\u6a21\u5757\uff09\u6392\u5e8f\u7684\u5411\u91cf\u662f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e3ca300d8666eb94fd4ddd22088e00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{b}|< \\begin{vmatrix}\\vv{a}\\end{vmatrix} < |\\vv{d}| < \\begin{vmatrix}\\vv{c}\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"144\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u786e\u5b9a\u539f\u70b9\u4e3a\u8be5\u70b9\u7684\u5411\u91cf\u7684\u5927\u5c0f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fa493d9071a18cc176e19c8aeda71e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6700\u540e\u4e00\u70b9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7da7d69ba3de7c0a400c5739021b3ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(7,-4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u5b83\u7684\u6a21\uff0c\u5fc5\u987b\u9996\u5148\u627e\u5230\u5411\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u51cf\u53bb\u6781\u503c\u51cf\u53bb\u539f\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-237f500f255108fb2f6673bdf1ac0c88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A=(7,-4)-(-3,2)=(10,-6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"337\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u5411\u91cf\uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528\u6a21\u6570\u516c\u5f0f\u8ba1\u7b97\u5176\u6a21\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c92f7a1361051e25fa90e0ed878a676_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\vv{AB} \\end{vmatrix} =\\sqrt{10^2+(-6)^2} = \\sqrt{100+36}=\\bm{\\sqrt{136}}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"340\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u5206\u89e3\u4ee5\u4e0b\u5411\u91cf\u5e76\u627e\u5230\u5176\u5206\u91cf\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-992e1cdc6a75b8bdfe860c97dc9911e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =8 \\qquad \\alpha = 45\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u77e2\u91cf\u7684\u6c34\u5e73\u5206\u91cf\u7b49\u4e8e\u6a21\u4e58\u4ee5\u89d2\u5ea6\u7684\u4f59\u5f26\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33aa199d1341f57e7a85abaa3c261a91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_x= \\lvert \\vv{a}\\rvert \\cdot \\text{cos}(45\u00ba)= 8 \\cdot 0,71 = 5,66\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5411\u91cf\u7684\u5782\u76f4\u5206\u91cf\u7b49\u4e8e\u6a21\u4e58\u4ee5\u89d2\u5ea6\u7684\u6b63\u5f26\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-269cf4eed12832856838538f0a314aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_y= \\lvert \\vv{a}\\rvert \\cdot \\text{sen}(45\u00ba)= 8 \\cdot 0,71 = 5,66\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u5411\u91cf\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9a4b542b5e7893c3da383ffa65a133b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{ = (5,66 \\ ,\\ 5,66)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u4e2a\u5206\u91cf\u662f\u76f8\u540c\u7684\uff0c\u5373\u77e2\u91cf\u7684\u503e\u659c\u89d2\u5ea6\u4e3a 45\u00b0\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u8ba1\u7b97\u4e0e\u4ee5\u4e0b\u5411\u91cf\u5177\u6709\u76f8\u540c\u65b9\u5411\u548c\u65b9\u5411\u4f46\u6a21\u6570\u4e3a 1 \u7684\u5411\u91cf\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-764894932cc153ee326360c077c75ec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a} = (-4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u65b9\u5411\u76f8\u540c\u3001\u65b9\u5411\u76f8\u540c\u4f46\u6a21\u4e3a1\u7684\u5411\u91cf\u4e3a\u5355\u4f4d\u5411\u91cf\u3002\u4e3a\u4e86\u8ba1\u7b97\u5b83\uff0c\u6211\u4eec\u9996\u5148\u6c42\u5411\u91cf\u7684\u6a21\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d067857f68bb43d3ee3693466272cc36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert=\\sqrt{(-4)^2+3^2} = \\sqrt{16+9} = \\sqrt{25} = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"315\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u5c06\u539f\u59cb\u5411\u91cf\u9664\u4ee5\u5176\u6a21\u6765\u8ba1\u7b97\u5355\u4f4d\u5411\u91cf\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff7322f3b35f78c5e151f4e7dc59eb98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{a}_u = \\cfrac{\\vv{a}}{\\lvert \\vv{a} \\rvert} = \\frac{(-4,3)}{5}= \\bm{\\left(-\\frac{4}{5},\\frac{3}{5} \\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"238\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e606<\/h3>\n<p>\u5bf9\u4ee5\u4e0b\u5411\u91cf\u8fdb\u884c\u5411\u91cf\u5206\u89e3\u5e76\u8ba1\u7b97\u5176\u5355\u4f4d\u5411\u91cf\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-305f67adc42d0194ae1c8bbca09484a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =6 \\qquad \\alpha = 20\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u5206\u89e3\u5411\u91cf\u5e76\u627e\u5230\u5b83\u7684\u5750\u6807\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-425294f0e8b14e63cf0d59c6fa95f367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_x= \\lvert \\vv{a}\\rvert \\cdot \\text{cos}(20\u00ba)= 6 \\cdot 0,94 = 5,64\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a795bfcb22419526d23f6d0ff419fdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_y= \\lvert \\vv{a}\\rvert \\cdot \\text{sen}(20\u00ba)= 6 \\cdot 0,34 = 2,05\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"266\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u5411\u91cf\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abc6fa01a5b562627b05dc37ad7f59d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}= (5,64 \\ ,\\ 2,05)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u9664\u4ee5\u5b83\u7684\u6a21\u5f97\u5230\u7684\u5411\u91cf\u6765\u8ba1\u7b97\u5355\u4f4d\u5411\u91cf\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-287411b8f47ca842a6db2cbe1c9a6ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{a}_u = \\cfrac{\\vv{a}}{\\lvert \\vv{a} \\rvert} = \\frac{(5,64 \\ ,\\ 2,05)}{6}= \\bm{(0,94 \\ , \\ 0,34) }\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u6ce8\u610f\uff0c\u5355\u4f4d\u5411\u91cf\u7684\u5206\u91cf\u7b49\u4e8e\u5b83\u4e0e X \u8f74\u5f62\u6210\u7684\u89d2\u5ea6\u7684\u4f59\u5f26\u548c\u6b63\u5f26\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u770b\u5230\u77e2\u91cf\u5927\u5c0f\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u5176\u516c\u5f0f\u8ba1\u7b97\u77e2\u91cf\u5927\u5c0f\u7684\u8bf4\u660e\u3002\u60a8\u8fd8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u4ece\u4e24\u70b9\u627e\u5230\u6a21\u5757\uff1a\u5176\u8d77\u70b9\u548c\u7ec8\u70b9 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e5%85%ac%e5%bc%8f%e7%9a%84%e6%a8%a1%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u5982\u4f55\u8ba1\u7b97\u5411\u91cf\u7684\u6a21<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[21],"tags":[],"class_list":["post-210","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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