{"id":71,"date":"2023-09-16T13:03:21","date_gmt":"2023-09-16T13:03:21","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e4%b8%aa%e5%90%91%e9%87%8f%e7%9a%84%e5%8f%89%e7%a7%af%e4%ba%a4%e5%8f%89%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/"},"modified":"2023-09-16T13:03:21","modified_gmt":"2023-09-16T13:03:21","slug":"%e4%b8%a4%e4%b8%aa%e5%90%91%e9%87%8f%e7%9a%84%e5%8f%89%e7%a7%af%e4%ba%a4%e5%8f%89%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e4%b8%aa%e5%90%91%e9%87%8f%e7%9a%84%e5%8f%89%e7%a7%af%e4%ba%a4%e5%8f%89%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\uff08\u6216\u53c9\u79ef\uff09"},"content":{"rendered":"<p>\u672c\u9875\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u4f7f\u7528\u53f3\u624b\u5b9a\u5219\uff08\u6216\u87ba\u65cb\u5f62\uff09\u627e\u5230\u53c9\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u60a8\u4f1a\u53d1\u73b0\u6b64\u7c7b\u64cd\u4f5c\u7684\u7528\u9014\uff0c\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u3001\u7ec3\u4e60\u548c\u95ee\u9898\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-producto-vectorial-de-dos-vectores\"><\/span>\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u53c9\u79ef<\/strong>\u662f\u4e09\u7ef4\u7a7a\u95f4\uff08\u5728 R3 \u4e2d\uff09\u4e2d\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u8fd0\u7b97\u3002\u8be5\u5411\u91cf\u8fd0\u7b97\u7684\u7ed3\u679c\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u5176\u65b9\u5411\u5782\u76f4\u4e8e\u4e24\u4e2a\u76f8\u4e58\u5411\u91cf\uff0c\u5e76\u4e14\u5176\u6a21\u7b49\u4e8e\u4e58\u6570\u5411\u91cf\u7684\u6a21\u4e0e\u5b83\u4eec\u5f62\u6210\u7684\u89d2\u5ea6\u7684\u6b63\u5f26\u7684\u4e58\u79ef\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u7684\u516c\u5f0f\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-625267c9d98347748a771c7cec9bfcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u516c\u5f0f\u4e2d\u770b\u5230\u7684\uff0c\u53c9\u79ef\u8868\u793a\u4e3a<\/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-850177c0489097bd9409ba9b13b07506_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\times}\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5b83\u4e5f\u88ab\u79f0\u4e3a<strong>\u53c9\u79ef\u3002<\/strong>\u5b83\u6709\u65f6\u4e5f\u88ab\u79f0\u4e3a\u5409\u5e03\u65af\u77e2\u91cf\u79ef\uff0c\u56e0\u4e3a\u4ed6\u53d1\u660e\u4e86\u5b83\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quel-est-le-produit-vectoriel-de-deux-vecteurs-.webp\" alt=\"\" class=\"wp-image-3883\" width=\"307\" height=\"310\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\u6240\u770b\u5230\u7684\uff0c\u53c9\u79ef\u5782\u76f4\u4e8e\u5b83\u4eec\u76f8\u4e58\u7684\u4e24\u4e2a\u5411\u91cf\uff0c\u56e0\u6b64\uff0c\u5b83\u5782\u76f4\u4e8e\u5305\u542b\u5b83\u4eec\u7684\u5e73\u9762\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-para-calcular-el-producto-vectorial-de-dos-vectores\"><\/span>\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u53c9\u79ef\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5982\u679c\u6211\u4eec\u77e5\u9053\u5411\u91cf\u7684\u7b1b\u5361\u5c14\u5750\u6807\uff0c\u8ba1\u7b97\u5b83\u4eec\u7684\u53c9\u79ef\u7684\u6700\u7b80\u5355\u65b9\u6cd5\u662f\u6c42\u89e3 3&#215;3 \u884c\u5217\u5f0f\u3002\u89c2\u5bdf\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u8003\u8651\u4efb\u610f\u4e24\u4e2a\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-581394386a4c68ca2bfa92fb4e2445ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (\\text{u}_x,\\text{u}_y,\\text{u}_z) \\qquad \\vv{\\text{v}}= (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5176\u5411\u91cf\u79ef\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-56551111a4f5a18a4609772ebaeaf919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5176\u4e2d\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-899f7cb82c85508ac2129e2393976f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}, \\vv{j},\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u8fd9\u4e9b\u5206\u522b\u662f X\u3001Y \u548c Z \u8f74\u65b9\u5411\u7684\u5355\u4f4d\u5411\u91cf\u3002<\/p>\n<\/div>\n<p>\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u53c9\u79ef\u7684\u793a\u4f8b\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-89a657062237b32001dad723a07ad2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,1,0) \\qquad \\vv{\\text{v}}= (2,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"227\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u786e\u5b9a\u5411\u91cf\u4e4b\u95f4\u7684\u5411\u91cf\u79ef\uff0c\u6211\u4eec\u5fc5\u987b\u505a\u51fa\u4ee5\u4e0b 3 \u9636\u884c\u5217\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-abc77b698bf6f4fddec1ab2dcc8b07f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; 1 &amp; 0 \\\\[1.1ex] 2 &amp;1&amp;-1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"145\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4f50\u5242\u6216\u8f85\u56e0\u5b50\u6765\u6c42\u89e3\u884c\u5217\u5f0f\uff08\u4e5f\u53ef\u4ee5\u4f7f\u7528 Sarrus \u89c4\u5219\uff09\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-eeeac04b3f0edd64e5413629051551fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; 1 &amp; 0 \\\\[1.1ex] 2 &amp;1&amp;-1 \\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 1 &amp; 0 \\\\[1.1ex] 1&amp;-1 \\end{vmatrix} -\\vv{j}\\begin{vmatrix}  3&amp;  0 \\\\[1.1ex] 2 &amp;-1 \\end{vmatrix}+\\vv{z}\\begin{vmatrix}3&amp; 1 \\\\[1.1ex] 2 &amp;1 \\end{vmatrix}  \\\\[2ex] &amp; = -\\vv{i}+3\\vv{j}+\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u5411\u91cf\u79ef\u7684\u7ed3\u679c\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-625f3af33d3cd3b9991682014c911024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(-1,3,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-la-direccion-y-el-sentido-del-producto-vectorial\"><\/span>\u786e\u5b9a\u53c9\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u65f6\u6211\u4eec\u4e0d\u9700\u8981\u77e5\u9053\u53c9\u79ef\u5f97\u5230\u7684\u5411\u91cf\u7684\u5206\u91cf\uff0c\u4f46\u53ea\u8981\u627e\u5230\u5b83\u7684\u6a21\u3001\u5b83\u7684\u65b9\u5411\u548c\u5b83\u7684\u65b9\u5411\u5c31\u8db3\u591f\u4e86\u3002\u8fd9\u5728\u7269\u7406\u5b66\u4e2d\u7ecf\u5e38\u53d1\u751f\uff0c\u5c24\u5176\u662f\u5728\u529b\u7684\u8ba1\u7b97\u4e2d\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6c42\u5411\u91cf\u4e58\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411\u6709\u591a\u79cd\u89c4\u5219\uff0c\u6700\u8457\u540d\u7684\u662f<strong>\u53f3\u624b\u5b9a\u5219<\/strong>\uff08\u7528\u4e09\u4e2a\u624b\u6307\u6216\u7528\u6574\u53ea\u624b\uff09\u548c<strong>\u87ba\u65cb\u5b9a\u5219\uff08\u6216\u87ba\u4e1d\uff09<\/strong> \u3002\u60a8\u53ef\u4ee5\u4f7f\u7528\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\uff0c\u56e0\u6b64\u60a8\u65e0\u9700\u4e86\u89e3\u6240\u6709\u89c4\u5219\uff0c\u6211\u4eec\u4ecd\u4f1a\u5411\u60a8\u89e3\u91ca\u8fd9\u4e09\u4e2a\u89c4\u5219\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u575a\u6301\u4f7f\u7528\u60a8\u6700\u559c\u6b22\u7684\u4e00\u4e2a\u3002 \ud83d\ude09<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-mano-derecha-3-dedos\"><\/span>\u53f3\u624b\u5b9a\u5219\uff083\u6307\uff09<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u53f3\u624b\u89c4\u5219\u6216\u5b9a\u5f8b\u7684\u4e09\u6307\u7248\u672c\u6d89\u53ca\u6267\u884c\u4ee5\u4e0b\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;\">\u5c06\u53f3\u624b\u7684\u98df\u6307\u653e\u5728\u53c9\u79ef\u7684\u7b2c\u4e00\u4e2a\u5411\u91cf\u4e0a\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u5c06\u53f3\u624b\u7684\u4e2d\u6307\uff08\u6216\u4e2d\u6307\uff09\u671d\u5411\u53c9\u79ef\u7684\u7b2c\u4e8c\u4e2a\u5411\u91cf\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acab6198e5d0337e7d0e9ed7814c16d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u751f\u6210\u7684\u62c7\u6307\u4f4d\u7f6e\u8868\u793a\u53c9\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-ou-loi-de-la-main-droite.webp\" alt=\"\" class=\"wp-image-892\" width=\"392\" height=\"353\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-mano-derecha-palma-de-la-mano\"><\/span>\u53f3\u624b\u5b9a\u5219\uff08\u624b\u638c\uff09<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u624b\u638c\u7248\u672c\u7684\u53f3\u624b\u89c4\u5219\u6216\u6cd5\u5219\u4e0e\u4e4b\u524d\u7684\u89c4\u5219\u975e\u5e38\u76f8\u4f3c\u3002\u8981\u5e94\u7528\u5b83\uff0c\u60a8\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\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;\">\u5c06\u53f3\u624b\u7684\u624b\u6307\u6307\u5411\u4e0e\u53c9\u79ef\u7684\u7b2c\u4e00\u4e2a\u5411\u91cf\u76f8\u540c\u7684\u65b9\u5411\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u5c06\u624b\u6307\u79fb\u5411\u53c9\u79ef\u7684\u7b2c\u4e8c\u4e2a\u5411\u91cf\uff0c\u5408\u4e0a\u53f3\u624b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acab6198e5d0337e7d0e9ed7814c16d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span>\u60a8\u9700\u8981\u5c06\u624b\u653e\u5728\u77e2\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff08\u6216\u8ddd\u79bb\uff09\u8f83\u5c0f\u7684\u4e00\u4fa7\u3002<\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u62c7\u6307\u7684\u6700\u7ec8\u4f4d\u7f6e\u51b3\u5b9a\u4e86\u53c9\u79ef\u7684\u65b9\u5411\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteur-produit-regle-de-droite.webp\" alt=\"\u53f3\u624b\u5c3a\u5b50\u77e2\u91cf\u4e58\u79ef\" class=\"wp-image-898\" width=\"373\" height=\"342\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-del-sacacorchos\"><\/span>\u5f00\u74f6\u5668\u89c4\u5219<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u87ba\u65cb\u5c3a\u6216\u87ba\u65cb\u5c3a<\/strong>\u7c7b\u4f3c\u4e8e\u4f7f\u7528\u6574\u4e2a\u624b\u638c\u7684\u53f3\u624b\u5c3a\u3002\u7a0b\u5e8f\u5982\u4e0b\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;\">\u53d1\u6325\u4f60\u7684\u60f3\u8c61\u529b\uff0c\u653e\u7f6e\u4e00\u4e2a\u5f00\u74f6\u5668\uff08\u6216\u87ba\u9489\uff09\uff0c\u5176\u624b\u67c4\u6307\u5411\u4e0e\u53c9\u79ef\u7684\u7b2c\u4e00\u4e2a\u5411\u91cf\u76f8\u540c\u7684\u65b9\u5411\u3002\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u7136\u540e\u5c06\u5f00\u74f6\u5668\u8f6c\u5411\u53c9\u79ef\u7684\u7b2c\u4e8c\u4e2a\u5411\u91cf\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c87e248254db96e4d2c996a62911e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span>\u5c31\u597d\u50cf\u4f60\u8981\u628a\u5b83\u653e\u8fdb\u8f6f\u6728\u585e\u91cc\u4e00\u6837\u3002\u60a8\u9700\u8981\u5c06\u5f00\u74f6\u5668\u8f6c\u5230\u5411\u91cf\u4e4b\u95f4\u8ddd\u79bb\u6700\u77ed\u7684\u4e00\u4fa7\u3002<\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u5f00\u74f6\u5668\u87ba\u65cb\u6307\u5411\u7684\u65b9\u5411\u5c06\u662f\u5411\u91cf\u4e58\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-du-tire-bouchon-ou-de-la-vis.webp\" alt=\"\u5f00\u74f6\u5668\u6216\u87ba\u65cb\u5c3a\" class=\"wp-image-902\" width=\"327\" height=\"500\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-producto-vectorial-de-dos-vectores\"><\/span>\u4e24\u4e2a\u5411\u91cf\u53c9\u79ef\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li><strong>\u53cd\u4ea4\u6362\u6027\uff1a<\/strong>\u5411\u91cf\u79ef\u4e2d\u6d89\u53ca\u7684\u5411\u91cf\u7684\u987a\u5e8f\u5e76\u4e0d\u662f\u65e0\u5173\u7d27\u8981\u7684\uff0c\u56e0\u4e3a\u7b26\u53f7\u6839\u636e\u5b83\u800c\u53d8\u5316\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-da6aeea2768e41a7e3630dc83ff1e31b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times\\vv{\\text{v}} = - \\vv{\\text{v}}\\times\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"119\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5173\u4e8e\u5411\u91cf\u52a0\u6cd5\u548c\u51cf\u6cd5\u7684<strong>\u5206\u914d\u5f8b<\/strong>\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-bfddca49d7ded207f392f54341fff56d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times(\\vv{\\text{v}}+\\vv{\\text{w}}) = \\vv{\\text{u}}\\times\\text{v}}+\\vv{\\text{u}}\\times \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" 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-68e08abafcbf4b05614819ca1a364a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times(\\vv{\\text{v}}-\\vv{\\text{w}}) = \\vv{\\text{u}}\\times\\text{v}}-\\vv{\\text{u}}\\times \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u9f50\u6b21\u6027<\/strong>\uff1a\u5c06\u53c9\u79ef\u7684\u5411\u91cf\u4e58\u4ee5\u6807\u91cf\uff08\u5b9e\u6570\uff09\u76f8\u5f53\u4e8e\u5c06\u53c9\u79ef\u7684\u7ed3\u679c\u4e58\u4ee5\u6240\u8ff0\u6807\u91cf\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-2ee3552bb6b72db4d30b4aa9f73e99a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}}) =  (k\\cdot \\vv{\\text{u}})\\times\\vv{\\text{v}}=\\vv{\\text{u}}\\times(k\\cdot\\vv{\\text{v}})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5411\u91cf\u79ef\u4ea7\u751f\u7684\u5411\u91cf<strong>\u5782\u76f4<\/strong>\u4e8e\u8fd0\u7b97\u4e2d\u6d89\u53ca\u7684\u4e24\u4e2a\u5411\u91cf\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-6a96345e09a0fdb952557c9138c72ac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} \\vv{\\text{u}} \\perp (\\vv{\\text{u}}\\times\\vv{\\text{v}}) \\\\[2ex] \\vv{\\text{v}} \\perp (\\vv{\\text{u}}\\times\\vv{\\text{v}}) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6b64\u5916\uff0c\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u6b63\u4ea4\uff0c\u5219\u6ee1\u8db3\u4ee5\u4e0b\u65b9\u7a0b\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-d49d463798c6381c9a8c065417ee3dbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\perp \\vv{\\text{v}} \\ \\longrightarrow \\ \\begin{cases} \\vv{\\text{u}} \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}})=0 \\\\[2ex] \\vv{\\text{v}} \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}})=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e24\u4e2a<strong>\u5e73\u884c\u5411\u91cf<\/strong>\u7684\u53c9\u79ef\u7b49\u4e8e\u96f6\u5411\u91cf\uff08\u6216\u96f6\uff09\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-5a2e4e335c132d024b2932139a51f101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\ || \\ \\vv{\\text{v}} \\ \\longrightarrow \\ \\vv{\\text{u}}\\times\\vv{\\text{v}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u6211\u4eec\u4e0d\u77e5\u9053\u4e24\u4e2a\u5411\u91cf\u5f62\u6210\u7684\u89d2\u5ea6\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u8ba1\u7b97\u5b83\u4eec\u7684\u5411\u91cf\u4e58\u79ef\u7684\u6a21\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-f27e24e2a7310fb1e727891c17de911a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}\\times\\vv{\\text{v}} \\rvert = \\sqrt{ \\lvert \\vv{\\text{u}}\\rvert ^2 \\cdot \\lvert \\vv{\\text{v}} \\rvert ^2 - (\\vv{\\text{u}}\\cdot \\vv{\\text{v}})^2 \\vphantom{\\frac{1}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"233\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-el-area-de-un-paralelogramo-o-un-triangulo-mediante-el-producto-vectorial\"><\/span>\u4f7f\u7528\u53c9\u79ef\u8ba1\u7b97\u5e73\u884c\u56db\u8fb9\u5f62\u6216\u4e09\u89d2\u5f62\u7684\u9762\u79ef<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u51e0\u4f55\u4e0a\uff0c\u4e24\u4e2a\u5411\u91cf\u53c9\u79ef\u7684\u6a21\u4e0e\u4ee5\u8fd9\u4e24\u4e2a\u5411\u91cf\u4e3a\u8fb9\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u4e00\u81f4\u3002\u56e0\u6b64\uff0c<strong>\u53c9\u79ef\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u3002<\/strong> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-de-deux-vecteurs-dans-lespace.webp\" alt=\"\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\" class=\"wp-image-929\" width=\"300\" height=\"173\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u53e6\u5916\uff0c\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u5bf9\u89d2\u7ebf\u5c06\u5176\u5206\u6210\u4e24\u4e2a\u4e09\u89d2\u5f62\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e09\u89d2\u5f62\u662f\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u4e00\u534a\u3002\u56e0\u6b64\uff0c<strong>\u4e09\u89d2\u5f62\u7684\u9762\u79ef<\/strong>\u662f\u4ee5\u5b83\u7684\u4e24\u6761\u8fb9\u4e3a\u5411\u91cf\u7684\u53c9\u79ef\u7684\u6a21\u6570\u7684\u4e00\u534a\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-de-deux-vecteurs-dans-r2.webp\" alt=\"r2 \u4e2d\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\" class=\"wp-image-927\" width=\"300\" height=\"173\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u56de\u60f3\u4e00\u4e0b\uff0c3 \u7ef4\u7a7a\u95f4\u4e2d\u5411\u91cf\u7684\u6a21\u662f\u5176\u5750\u6807\u5e73\u65b9\u548c\u7684\u6839\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-8cf7995798482007ea32b809e80a4062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert =  \\sqrt{\\vphantom{\\frac{1}{2}} \\text{v}_x^2+\\text{v}_y^2+\\text{v}_z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"155\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p>\u8fd9\u662f\u4e24\u4e2a\u5411\u91cf\u53c9\u79ef\u5728\u6570\u5b66\u9886\u57df\u7684\u4e24\u4e2a\u5e94\u7528\u3002\u7136\u800c\uff0c\u5b83\u8fd8\u6709\u5176\u4ed6\u7528\u9014\uff0c\u4f8b\u5982\u5728\u7269\u7406\u5b66\u4e2d\u5b83\u7528\u4e8e\u8ba1\u7b97\u78c1\u573a\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-productos-vectoriales-de-vectores\"><\/span>\u89e3\u51b3\u4e86\u5411\u91cf\u7684\u5411\u91cf\u79ef\u7684\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\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u53c9\u79ef\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-a1c06e6d75f54661416056d31d409d8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (-1,4,2) \\qquad \\vv{\\text{v}}= (0,-2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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\">\u4e3a\u4e86\u786e\u5b9a\u5411\u91cf\u4e4b\u95f4\u7684\u5411\u91cf\u79ef\uff0c\u6211\u4eec\u5fc5\u987b\u6c42\u89e3\u4ee5\u4e0b\u7ef4\u5ea6\u4e3a 3\u00d73 \u7684\u884c\u5217\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-44db63ee02936f6e5f21891c3e412fb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] -1&amp; 4 &amp; 2 \\\\[1.1ex] 0 &amp;-2&amp;1  \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"160\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4f50\u5242\u6216\u8f85\u56e0\u5b50\u6765\u6c42\u89e3\u884c\u5217\u5f0f\uff08\u4f46\u4e5f\u53ef\u4ee5\u4f7f\u7528\u8428\u52d2\u65af\u89c4\u5219\uff09\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-fe298c37814c92498e4fd8ade0620951_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] -1&amp; 4 &amp; 2 \\\\[1.1ex] 0 &amp;-2&amp;1\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 4 &amp; 2 \\\\[1.1ex]-2&amp;1\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  -1&amp; 2 \\\\[1.1ex] 0 &amp;1\\end{vmatrix}+\\vv{z}\\begin{vmatrix}-1&amp; 4 \\\\[1.1ex] 0 &amp;-2\\end{vmatrix}  \\\\[2ex] &amp; = 8\\vv{i}+\\vv{j}+2\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"387\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u5411\u91cf\u79ef\u7684\u7ed3\u679c\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-a1efe3e9fce5a83e193da24a5ff60835_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(8,1,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" 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>\u6c42\u4ee5\u4e0b\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u53c9\u79ef\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-210c7ec7b29e06198c491e83e7825a42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,-2,4) \\qquad \\vv{\\text{v}}= (1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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\">\u4e3a\u4e86\u627e\u5230\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5411\u91cf\u79ef\uff0c\u6211\u4eec\u5fc5\u987b\u6c42\u89e3\u4ee5\u4e0b 3\u00d73 \u884c\u5217\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-6a23d8e45f9065f70c576e6b8db02465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -2 &amp; 4 \\\\[1.1ex] 1 &amp;5&amp;-3  \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4f34\u968f\u6216\u8f85\u56e0\u5b50\u6c42\u89e3\u884c\u5217\u5f0f\uff08\u5c3d\u7ba1\u8428\u9c81\u65af\u89c4\u5219\u53ef\u4ee5\u4e92\u6362\u4f7f\u7528\uff09\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-02ffb40666893faa7677234065f3f85f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -2 &amp; 4 \\\\[1.1ex] 1 &amp;5&amp;-3\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} -2 &amp; 4 \\\\[1.1ex] 5&amp;-3\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  3&amp; 4 \\\\[1.1ex]  1&amp;-3\\end{vmatrix}+\\vv{z}\\begin{vmatrix}3&amp; -2  \\\\[1.1ex] 1 &amp;5\\end{vmatrix}  \\\\[2ex] &amp; = -14\\vv{i}+13\\vv{j}+17\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"386\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5411\u91cf\u79ef\u7684\u7ed3\u679c\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-a8f7c253fdd7c5be3635a42a3826acfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(-14,13,17)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" 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\u4e603<\/h3>\n<p>\u77e5\u9053\u4e24\u4e2a\u5411\u91cf\u7684\u6a21\u53ca\u5176\u5f62\u6210\u7684\u89d2\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-b632ab1324e7ece2d4c1f5c54249b425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{\\text{u}}|= 5 \\qquad |\\vv{\\text{v}}|= 6 \\qquad \\alpha = 30\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"226\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u786e\u5b9a\u4e24\u4e2a\u5411\u91cf\u53c9\u79ef\u7684\u5927\u5c0f\u3002 <\/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\">\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u8f7b\u677e\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5411\u91cf\u79ef\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-06dcff41e0dcf31152f0047507056f24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert &amp; = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha) \\\\[2ex] &amp; = 5 \\cdot 6 \\cdot \\text{sen}(30\u00ba) \\\\[2ex] &amp;= 30 \\cdot 0,5 \\\\[2ex] &amp;= \\bm{15} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"186\" style=\"vertical-align: 0px;\"><\/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>\u6765\u81ea\u5c4f\u5e55\u5e73\u9762\u4e2d\u5305\u542b\u7684\u4ee5\u4e0b\u5411\u91cf\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-en-ligne-de-deux-vecteurs.webp\" alt=\"\u4e24\u4e2a\u76f4\u7ebf\u5411\u91cf\u7684\u53c9\u79ef\" class=\"wp-image-938\" width=\"151\" height=\"231\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u8ba1\u7b97\u7531\u4ee5\u4e0b\u5411\u91cf\u8fd0\u7b97\u4ea7\u751f\u7684\u5411\u91cf\u7684\u5927\u5c0f\u3001\u65b9\u5411\u548c\u65b9\u5411\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-facaf3cf3a645b725e61c9fcb195e53c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" 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\">\u8fd9\u4e24\u4e2a\u5411\u91cf\u662f\u5782\u76f4\u7684\uff0c\u56e0\u6b64\u5411\u91cf\u79ef\u7684\u8303\u6570\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-d8f675fe7eb44c050c508c4771c0a439_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert &amp; = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha) \\\\[2ex] &amp; = 3 \\cdot 4 \\cdot \\text{sen}(90\u00ba) \\\\[2ex] &amp;= 12 \\cdot 1 \\\\[2ex] &amp;= \\bm{12} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u77e2\u91cf\u4e58\u79ef\u5f97\u5230\u7684\u77e2\u91cf\u5782\u76f4\u4e8e\u53c2\u4e0e\u8fd0\u7b97\u7684\u4e24\u4e2a\u77e2\u91cf\uff0c<strong>\u56e0\u6b64\u5176\u65b9\u5411\u5c06\u5782\u76f4\u4e8e\u5c4f\u5e55\u3002<\/strong><\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4f7f\u7528\u76f4\u7ebf\uff08\u6216\u87ba\u65cb\uff09\u89c4\u5219\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad<strong>\u51fa\u7ed3\u679c\u5411\u91cf\u7684\u65b9\u5411\u5c06\u671d\u5411\u5c4f\u5e55\u5185\u90e8\u3002<\/strong><\/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\u4ee5\u4e0b\u5217\u5411\u91cf\u4f5c\u4e3a\u5176\u4e24\u6761\u8fb9\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\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-43326a03cb829fb91d8c265bddf92b8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (2,3,-2) \\qquad \\vv{\\text{v}}= (5,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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\">\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u4e0e\u5f62\u6210\u5b83\u7684\u5411\u91cf\u53c9\u79ef\u7684\u6a21\u91cd\u5408\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u5411\u91cf\u7684\u5411\u91cf\u79ef\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-0e7c1825be82d94c4eae49c73f509858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}}\\times \\vv{\\text{v}} = \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex]2&amp; 3 &amp; -2 \\\\[1.1ex] 5 &amp;0&amp;-1\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 3 &amp; -2 \\\\[1.1ex] 0&amp;-1\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  2&amp; -2 \\\\[1.1ex] 5 &amp;-1\\end{vmatrix}+\\vv{z}\\begin{vmatrix}2&amp; 3  \\\\[1.1ex] 5 &amp;0\\end{vmatrix}  \\\\[2ex] &amp; = -3\\vv{i}-8\\vv{j}-15\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u662f\u4f60\u7684\u6a21\u5757\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-164e46102f5d27babfec98f25d479fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\sqrt{\\vphantom{\\frac{1}{2}} (-3)^2+(-8)^2+(-15)^2}=\\bm{17,26} \\ \\mathbf{u}\\bm{^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"404\" style=\"vertical-align: -10px;\"><\/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>\u6c42\u4ee5\u4e0b\u5217\u70b9\u4e3a\u9876\u70b9\u7684\u4e09\u89d2\u5f62\u7684\u9762\u79ef\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-dc08f9ac339b7ac3787a449cf5558c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1,0) \\qquad B(4,0,3)\\qquad C(-1,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"294\" 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\u5fc5\u987b\u8ba1\u7b97\u5f62\u6210\u4e09\u89d2\u5f62\u8fb9\u7684\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-f7661fc5ae3b35c76e0fe98203258962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (4,0,3)-(2,1,0) = (2,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"351\" 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-5d3f55a240188777fdbb3d74cbf4f61f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} =C- B =(-1,2,3)- (4,0,3) = (-5,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"366\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u662f\u6784\u6210\u5b83\u7684\u5411\u91cf\u7684\u5411\u91cf\u4e58\u79ef\u7684\u4e00\u534a\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u5411\u91cf\u7684\u5411\u91cf\u79ef\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-42a0ae5858bcb681ee92ec1ed67424c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}}\\times \\vv{\\text{v}} = \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex]2&amp; -1 &amp; 3 \\\\[1.1ex] -5 &amp;2&amp;0\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} -1 &amp; 3 \\\\[1.1ex] 2&amp;0\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  2&amp;  3 \\\\[1.1ex] -5 &amp;0\\end{vmatrix}+\\vv{z}\\begin{vmatrix}2&amp; -1  \\\\[1.1ex] -5 &amp;2\\end{vmatrix}  \\\\[2ex] &amp; = -6\\vv{i}-15\\vv{j}-\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u4f60\u7684\u6a21\u5757\u4e4b\u540e\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-4a52c4a997a5b68d67b9ae52ca599661_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\sqrt{\\vphantom{\\frac{1}{2}} (-6)^2+(-15)^2+(-1)^2}=16,19\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"342\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u5c06\u662f\u6a21\u5757\u7684\u4e00\u534a\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-b56f201265ba609f4b7c75f486120fc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\cfrac{1}{2}\\cdot  \\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\cfrac{1}{2}\\cdot 16,19=\\bm{8,09} \\ \\mathbf{u}\\bm{^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"284\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9875\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u4f7f\u7528\u53f3\u624b\u5b9a\u5219\uff08\u6216\u87ba\u65cb\u5f62\uff09\u627e\u5230\u53c9\u79ef\u7684\u65b9\u5411\u548c\u65b9\u5411\u3002\u66f4\u91cd &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%b8%a4%e4%b8%aa%e5%90%91%e9%87%8f%e7%9a%84%e5%8f%89%e7%a7%af%e4%ba%a4%e5%8f%89%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\uff08\u6216\u53c9\u79ef\uff09<\/span> \u67e5\u770b\u5168\u6587 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