{"id":254,"date":"2023-07-10T09:19:33","date_gmt":"2023-07-10T09:19:33","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%85%ac%e5%bc%8f%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%9b%b8%e4%ba%a4%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb\/"},"modified":"2023-07-10T09:19:33","modified_gmt":"2023-07-10T09:19:33","slug":"%e5%85%ac%e5%bc%8f%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%9b%b8%e4%ba%a4%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%85%ac%e5%bc%8f%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%9b%b8%e4%ba%a4%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb\/","title":{"rendered":"\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u786e\u5b9a\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u7ec3\u4e60\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-son-dos-rectas-que-se-cruzan\"><\/span>\u4ec0\u4e48\u662f\u4e24\u6761\u76f8\u4ea4\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e4b\u524d\uff0c\u8ba9\u6211\u4eec\u7b80\u5355\u56de\u987e\u4e00\u4e0b\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u8fd9\u79cd\u76f8\u5bf9\u4f4d\u7f6e\u5230\u5e95\u7531\u4ec0\u4e48\u7ec4\u6210\uff1a <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p><strong>\u4e24\u6761\u76f8\u4ea4\u7ebf\uff0c\u4e5f\u79f0\u4e3a\u76f8\u4ea4\u7ebf\uff0c\u662f\u4e24\u6761\u65b9\u5411\u4e0d\u540c\u4e14\u5728\u4efb\u4f55\u4e00\u70b9\u90fd\u4e0d\u76f8\u4ea4\u7684\u4e0d\u540c\u76f4\u7ebf<\/strong>\u3002\u56e0\u6b64\uff0c\u4e24\u6761\u4ea4\u53c9\u7ebf\u4e0d\u5728\u540c\u4e00\u5e73\u9762\u4e0a\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\/lignes-dintersection-1.webp\" alt=\"\u4e0e 2 \u4e2a bin \u76f8\u4ea4\u7684\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\" class=\"wp-image-2692\" width=\"227\" height=\"223\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u5728\u7ebf\u4e0a\u65b9\u7684\u56fe\u5f62\u8868\u793a\u4e2d<\/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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u603b\u662f\u8d70\u5728\u524d\u9762<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u6240\u4ee5\u4ed6\u4eec\u6c38\u8fdc\u4e0d\u4f1a\u4e92\u76f8\u63a5\u89e6\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-distancia-entre-dos-rectas-que-se-cruzan\"><\/span>\u5982\u4f55\u8ba1\u7b97\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb<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-106\"><\/div>\n<\/div>\n<p>\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u786e\u5b9a\u7a7a\u95f4\u4e2d\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u672c\u9875\u6211\u4eec\u53ea\u8bb2\u89e3\u4e00\u79cd\u6700\u7b80\u5355\u7684\u65b9\u6cd5\uff0c\u56e0\u4e3a\u53e6\u5916\u4e24\u79cd\u65b9\u6cd5\u8f83\u957f\u4e14\u8f83\u590d\u6742\uff0c\u5b9e\u9645\u4e0a\u5f88\u5c11\u4f7f\u7528\u3002 <\/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\">\u8bbe\u65b9\u5411\u5411\u91cf\u548c\u4e24\u6761\u76f8\u4ea4\u7ebf\u7684\u4efb\u610f\u70b9\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-569f8d554a0f3704d247862d0b8ef852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} \\\\[2ex] A\\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}} \\\\[2ex] B\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"210\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"><strong>\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u516c\u5f0f<\/strong>\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" 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-dbc3e38427d29b2f4444ea732f955500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u5411\u91cf\u6df7\u5408\u79ef\u7684\u7edd\u5bf9\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4ee5\u53ca\u7531\u70b9\u5b9a\u4e49\u7684\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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/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-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002\u53e6\u4e00\u65b9\u9762\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a151f35eca7cc81494de906050e773fa_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>\u662f\u4e24\u6761\u4ea4\u53c9\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u7684\u5411\u91cf\u79ef\u7684\u5927\u5c0f\u3002<\/p>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u8981\u627e\u5230\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u60a8\u9700\u8981\u77e5\u9053\u5982\u4f55\u8ba1\u7b97<a href=\"https:\/\/mathority.org\/cn\/\u4e09\u4e2a\u5411\u91cf\u6216\u4e09\u91cd\u6807\u91cf\u79ef\u7684\u6df7\u5408\u79ef\u793a\u4f8b\/\">\u4e09\u91cd\u70b9\u79ef<\/a>\uff08\u6216\u4e09\u4e2a\u5411\u91cf\u7684\u6df7\u5408\u79ef\uff09\u548c<a href=\"https:\/\/mathority.org\/cn\/\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u4ea4\u53c9\u516c\u5f0f\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u5411\u91cf\u79ef<\/a>\uff08\u6216\u4e24\u4e2a\u5411\u91cf\u7684\u5411\u91cf\u79ef\uff09\u3002\u60a8\u53ef\u4ee5\u5728\u524d\u9762\u7684\u94fe\u63a5\u4e2d\u67e5\u770b\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u627e\u5230\u76f8\u5e94\u7684\u516c\u5f0f\u3001\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-distancia-entre-dos-rectas-que-se-cruzan\"><\/span>\u5982\u4f55\u67e5\u627e\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u793a\u4f8b<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>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5982\u4f55\u786e\u5b9a\u4e24\u6761\u4ea4\u53c9\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u4e00\u4e2a\u95ee\u9898\u4f5c\u4e3a\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u63a5\u4e0b\u6765\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u591a\u5c11\uff1f<\/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-6c4b9507f6e33691e0b89d18dac941cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  \\cfrac{x-1}{2} = \\cfrac{y-2}{4} = \\cfrac{z+2}{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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-c6dac5d90c57534aa97625685e0d60fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\  \\cfrac{x-3}{1} = \\cfrac{y+1}{3} = \\cfrac{z-1}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8bc6\u522b\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u70b9\u3002\u4e24\u6761\u76f4\u7ebf\u4ee5\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u56e0\u6b64\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-8b990f78d0263975304586abbd330167_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(2,4,-1) \\\\[2ex] A(1,2,-2) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(1,3,-2) \\\\[2ex] B(3,-1,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5e94\u7528\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u9762\u6211\u4eec\u89e3\u51b3\u6df7\u5408\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-3238f24b114cb49bf33dd66bccad1ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (3,-1,1) - (1,2,-2) = (2,-3,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" 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-c52c12945d04e320e688caf714569113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\\\[1.1ex] 2&amp;-3&amp;3 \\end{vmatrix}\\right| = \\left| -13 \\right| =13\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"321\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u6c42\u51fa\u5411\u91cf\u79ef\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-71afa7d4b49e542300c12b5263858665_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] 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\end{vmatrix}=-5\\vv{i} +3\\vv{j}+2\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"278\" style=\"vertical-align: 0px;\"><\/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-3c940dca4c85f7176555de5861b8f391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{5^2+3^2+2^2} = \\sqrt{25+9+4} = \\sqrt{38}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u516c\u5f0f\u4e2d\u6bcf\u4e00\u9879\u7684\u503c\u66ff\u6362\u4e3a\u4e24\u6761\u4ea4\u53c9\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-b0aac39997c35738e8e84a29ff7c97c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{13}{\\sqrt{38}}= \\bm{2,11}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"273\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-distancias-entre-dos-rectas-que-se-cruzan\"><\/span>\u89e3\u51b3\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6c42\u4ee5\u4e0b\u4e24\u6761\u76f8\u4ea4\u4e8e\u4e00\u70b9\u7684\u76f4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-265216663967ca7073a6662f565a3002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  \\cfrac{x-1}{2} = \\cfrac{y+1}{1} = \\cfrac{z+3}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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-30a48084a49d510c4d1b3693aa4fe2c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\  \\cfrac{x-2}{3} = \\cfrac{y-4}{-1} = \\cfrac{z-1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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\u9700\u8981\u627e\u5230\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u4e00\u4e2a\u70b9\u3002\u4e24\u6761\u76f4\u7ebf\u4ee5\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u56e0\u6b64\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-c9c49971e843f325a05b679decc761fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(2,1,2) \\\\[2ex] A(1,-1,-3) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(3,-1,2) \\\\[2ex] B(2,4,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"382\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u786e\u5b9a\u6df7\u5408\u4e58\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-7aebfb9bcb2e9dba46ba0e230db85d13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,4,1) - (1,-1,-3) = (1,5,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-7cbbf07d92c61e9042c470cf0998979b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} 2&amp;1&amp;2 \\\\[1.1ex] 3&amp;-1&amp;2 \\\\[1.1ex] 1&amp;5&amp;4 \\end{vmatrix}\\right| = \\left| -6 \\right| =6\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"289\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8ba1\u7b97\u53c9\u79ef\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-81ec8597a0394de740288b45f02f83fe_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] 2&amp;1&amp;2 \\\\[1.1ex] 3&amp;-1&amp;2 \\end{vmatrix}=4\\vv{i} +2\\vv{j}-5\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"265\" style=\"vertical-align: 0px;\"><\/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-d19b4508ad9d0abf5351ed01e69a9ed1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{4^2+2^2+(-5)^2} = \\sqrt{16+4+25} = \\sqrt{45}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"393\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u516c\u5f0f\u4e2d\u6bcf\u4e00\u9879\u7684\u503c\u66ff\u6362\u4e3a\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-fd922136a96374c8e63c8fd2f9d5b75f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{6}{\\sqrt{45}}= \\bm{0,89}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"274\" 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\u4e602<\/h3>\n<p>\u8ba1\u7b97\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-37d7980f4d797bacd8c0e89700ca8bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  \\cfrac{x-2}{3} = \\cfrac{y-4}{1} = \\cfrac{z+2}{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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-62d204b920ee51734407050000ba292a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\  \\cfrac{x+1}{2} = \\cfrac{y+2}{-2} = \\cfrac{z-1}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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\u9700\u8981\u8bc6\u522b\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u70b9\u3002\u4e24\u6761\u76f4\u7ebf\u4ee5\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u56e0\u6b64\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-0a143aef931b384aa35ce90cce508e6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(3,1,-1) \\\\[2ex] A(2,4,-2) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(2,-2,5) \\\\[2ex] B(-1,-2,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u786e\u5b9a\u6df7\u5408\u4e58\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-bd6405404fbdff4444a2ef50960ebf92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (-1,-2,1) - (2,4.-2) = (-3,-6,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"411\" 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-416d4c694479118b488d6d2ce919065e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} 3&amp;1&amp;-1 \\\\[1.1ex] 2&amp;-2&amp;5 \\\\[1.1ex] -3&amp;-6&amp;3 \\end{vmatrix}\\right| = \\left| 69 \\right| =69\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"321\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8ba1\u7b97\u53c9\u79ef\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-6c1fdd9699f2e2afea5f0e22d66893d4_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;-1 \\\\[1.1ex] 2&amp;-2&amp;5 \\end{vmatrix}=3\\vv{i} -17\\vv{j}-8\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"287\" style=\"vertical-align: 0px;\"><\/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-455404242cbc6840c272528679a162f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{3^2+(-17)^2+(-8)^2} = \\sqrt{9+289+64} = \\sqrt{362}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"447\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u516c\u5f0f\u4e2d\u6bcf\u4e2a\u672a\u77e5\u6570\u7684\u503c\u66ff\u6362\u4e3a\u4e24\u6761\u4ea4\u53c9\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-c6c7bf4bd93325deb60c6b700a80d57a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{69}{\\sqrt{362}}= \\bm{3,63}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"283\" 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\u4e603<\/h3>\n<p>\u6c42\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-abb15a9455ed23548309cfd3984be869_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\  \\begin{cases} x= -4t \\\\[1.7ex] y=2+3t \\\\[1.7ex] z=-1+t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"128\" style=\"vertical-align: 0px;\"><\/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-54a554e7979240b544ab677d73edfbcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\  (x,y,z)=(4,2,1)+t(3,2,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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\u9700\u8981\u627e\u5230\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u4e00\u4e2a\u70b9\u3002\u6b63\u786e\u7684<\/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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u76f4\u7ebf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u5411\u91cf\u65b9\u7a0b\u5f62\u5f0f\uff0c\u56e0\u6b64\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-d16fe0b303ba2b4875f8306008c4277c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(-4,3,1) \\\\[2ex] A(0,2,-1) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(3,2,-5) \\\\[2ex] B(4,2,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u786e\u5b9a\u4e09\u91cd\u6807\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-229bcf34e10eb9029765f7c135db7378_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (4,2,-1) - (0,2,1) = (4,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-bdaf8f04e3e0eb0f17938c92ce9a69e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} -4&amp;3&amp;1 \\\\[1.1ex] 3&amp;2&amp;-5 \\\\[1.1ex] 4&amp;0&amp;-2 \\end{vmatrix}\\right| = \\left| -34 \\right| =34\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"321\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8ba1\u7b97\u53c9\u79ef\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-94e9d9a0e4f15b3f0070dc300fbd6a1b_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] -4&amp;3&amp;1 \\\\[1.1ex] 3&amp;2&amp;-5 \\end{vmatrix}=-17\\vv{i} -17\\vv{j}-17\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"318\" style=\"vertical-align: 0px;\"><\/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-3c0c1d091a3b9b5686d05dd36e8c6a49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{(-17)^2+(-17)^2+(-17)^2} = \\sqrt{289+289+289} = \\sqrt{867}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"519\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u516c\u5f0f\u4e2d\u6bcf\u4e00\u9879\u7684\u503c\u66ff\u6362\u4e3a\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-24c2bf25fda88fa389cccd30c91db9d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{34}{\\sqrt{867}}= \\bm{1,15}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"282\" style=\"vertical-align: -17px;\"><\/p>\n<\/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\u4e86\u89e3\u5982\u4f55\u786e\u5b9a\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%85%ac%e5%bc%8f%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%9b%b8%e4%ba%a4%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb\/\"> <span class=\"screen-reader-text\">\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09<\/span> 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