{"id":268,"date":"2023-07-10T02:22:55","date_gmt":"2023-07-10T02:22:55","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%bb%80%e4%b9%88%e6%98%af%e5%90%91%e9%87%8f-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86-%e4%be%8b%e5%ad%90\/"},"modified":"2023-07-10T02:22:55","modified_gmt":"2023-07-10T02:22:55","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e5%90%91%e9%87%8f-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86-%e4%be%8b%e5%ad%90","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%bb%80%e4%b9%88%e6%98%af%e5%90%91%e9%87%8f-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86-%e4%be%8b%e5%ad%90\/","title":{"rendered":"\u4ec0\u4e48\u662f\u5411\u91cf\uff08\u6570\u5b66\uff09\uff1f"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5411\u91cf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u4eec\u662f\u4ec0\u4e48\u3001\u5b83\u4eec\u7684\u7279\u5f81\u3001\u5b83\u4eec\u5982\u4f55\u8ba1\u7b97\u3001\u5982\u4f55\u5bf9\u5411\u91cf\u8fdb\u884c\u8fd0\u7b97\u3001\u5b58\u5728\u7684\u4e0d\u540c\u7c7b\u578b\u2026\u2026<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-vector\"><\/span>\u4ec0\u4e48\u662f\u5411\u91cf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5411\u91cf\u7684\u6570\u5b66\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p>\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u5411\u91cf\u662f\u4ece\u4e00\u4e2a\u70b9\uff08\u79f0\u4e3a\u539f\u70b9\uff09\u5230\u53e6\u4e00\u70b9\uff08\u79f0\u4e3a\u7ec8\u70b9\uff09\u7684\u6709\u5411\u7ebf\u6bb5\u3002<\/strong><\/p>\n<p>\u4f8b\u5982\uff0c\u5728\u4e0b\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\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-243865b783ec40e03ec861ac2ebcb279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4ee5 A \u70b9\u4e3a\u539f\u70b9\uff0c\u4ee5 B \u70b9\u4e3a\u7ec8\u70b9\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\/quest-ce-quun-vecteur.webp\" alt=\"\u4ec0\u4e48\u662f\u6570\u5b66\u5411\u91cf\" class=\"wp-image-3678\" width=\"176\" height=\"176\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u77e2\u91cf\u4e3b\u8981\u7528\u4e8e\u6570\u5b66\uff08\u7279\u522b\u662f\u51e0\u4f55\u5b66\uff09\u548c\u7269\u7406\u5b66\u4e2d\uff0c\u4ee5\u56fe\u5f62\u65b9\u5f0f\u8868\u793a\u77e2\u91cf\u529b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-un-vector\"><\/span>\u5411\u91cf\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u4e86\u5411\u91cf\u7684\u6570\u5b66\u542b\u4e49\u540e\uff0c\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5b83\u4eec\u7684\u5c5e\u6027\u662f\u4ec0\u4e48\u3002<\/p>\n<p>\u6bcf\u4e2a\u5411\u91cf\u5177\u6709\u4ee5\u4e0b\u51e0\u4f55\u7279\u5f81\uff1a<\/p>\n<ul>\n<li><strong>\u65b9\u5411<\/strong>\uff1a\u77e2\u91cf\u7684\u65b9\u5411\u662f\u5305\u542b\u8be5\u77e2\u91cf\u7684\u7ebf\u6216\u4e0e\u5176\u5e73\u884c\u7684\u4efb\u4f55\u7ebf\u7684\u65b9\u5411\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5411\u91cf\u7684\u65b9\u5411\u5c31\u662f\u5b83\u6240\u5728\u7684\u7ebf\u3002<\/li>\n<li><strong>\u65b9\u5411<\/strong>\uff1a\u5411\u91cf\u7684\u65b9\u5411\u662f\u8be5\u5411\u91cf\u7684\u65b9\u5411\uff0c\u7531\u5176\u7bad\u5934\u6307\u793a\u3002<\/li>\n<li><strong>\u6a21<\/strong>\uff08\u6216\u5e45\u5ea6\uff09\uff1a\u5411\u91cf\u7684\u6a21\u662f\u5176\u957f\u5ea6\uff0c\u5bf9\u5e94\u4e8e\u5411\u91cf\u7684\u6570\u503c\u3002\u56e0\u6b64\uff0c\u5411\u91cf\u5747\u503c\u8d8a\u5927\uff0c\u4ee3\u8868\u7684\u5411\u91cf\u91cf\u5c31\u8d8a\u5927\u3002<\/li>\n<li><strong>\u5e94\u7528\u70b9<\/strong>\uff1a\u77e2\u91cf\u7684\u5e94\u7528\u70b9\u662f\u8be5\u77e2\u91cf\u7684\u539f\u70b9\u3002 <\/li>\n<\/ul>\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\/caracteristiques-d-un-vecteur.webp\" alt=\"\u5411\u91cf\u7684\u51e0\u4f55\u7279\u5f81\" class=\"wp-image-3682\" width=\"332\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u65b9\u5411\u548c\u5411\u91cf\u65b9\u5411\u7684\u6982\u5ff5\u7ecf\u5e38\u4ee4\u4eba\u56f0\u60d1\uff0c\u56e0\u6b64\u533a\u5206\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02\u5f88\u91cd\u8981\u3002\u770b\u4e0b\u9762\u7684\u4f8b\u5b50\uff0c\u6709\u4e24\u4e2a\u5411\u91cf\uff0c\u5b83\u4eec\u7684\u65b9\u5411\u76f8\u540c\uff0c\u4f46\u542b\u4e49\u4e0d\u540c\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\/sens-et-direction-d-un-vecteur.webp\" alt=\"\u5411\u91cf\u7684\u610f\u4e49\u548c\u65b9\u5411\u7684\u610f\u4e49\" class=\"wp-image-3686\" width=\"446\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u8fd9\u4e24\u4e2a\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u5e73\u884c\u7684\u3002\u76f8\u53cd\uff0c\u4ed6\u4eec\u7684\u65b9\u5411\u662f\u76f8\u53cd\u7684\uff0c\u56e0\u4e3a\u4ed6\u4eec\u9762\u5411\u540e\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"componentes-de-un-vector\"><\/span> \u5411\u91cf\u7684\u7ec4\u6210\u90e8\u5206<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u5411\u91cf\u7528\u7bad\u5934\u56fe\u5f62\u8868\u793a\uff0c\u4f46\u5411\u91cf\u4e5f\u53ef\u4ee5\u7528\u5411\u91cf\u7684\u5206\u91cf\uff08\u6216\u5750\u6807\uff09\u6570\u5b57\u8868\u793a\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5728\u56fe\u4e2d\u8868\u793a\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\/vecteur-exemples.webp\" alt=\"\u5411\u91cf\u7684\u4f8b\u5b50\" class=\"wp-image-3692\" width=\"316\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u8981\u8ba1\u7b97\u5411\u91cf\u7684\u5206\u91cf\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u786e\u5b9a\u5176\u539f\u70b9\u548c\u7ec8\u70b9\u7684\u5750\u6807\uff0c\u5373\u5411\u91cf\u7684\u8d77\u70b9\u548c\u7ec8\u70b9\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5411\u91cf\u7684\u539f\u70b9\u548c\u7ec8\u70b9\u662f\uff1a<\/p>\n<p class=\"has-text-align-center\">\u5411\u91cf\u539f\u70b9\uff1aA(2,1)<\/p>\n<p class=\"has-text-align-center\">\u77e2\u91cf\u7ec8\u70b9\uff1aB(5,6)<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u627e\u5230\u5411\u91cf\u7684\u5750\u6807\u6216\u5206\u91cf\uff0c\u53ea\u9700\u51cf\u53bb\u7ec8\u70b9\u51cf\u53bb\u539f\u70b9\u5373\u53ef\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-fba10729c8ded7f7c7051cfda5c12eab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{AB} &amp; = B- A \\\\[2ex] &amp; = (5,6)- (2,1) \\\\[2ex] &amp;= (5-2 \\ , \\ 6-1) \\\\[2ex] &amp;= (3,5) \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"144\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u56fe\u4e2d\u8868\u793a\u7684\u5411\u91cf\u7684\u5206\u91cf\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-8fbf31faea8cf602f9556fa80f618515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\bm{AB}}\\bm{=(3,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"operaciones-con-vectores\"><\/span>\u5411\u91cf\u8fd0\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"suma-de-vectores\"><\/span>\u6dfb\u52a0\u5411\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8981\u5bf9\u4e24\u4e2a\u5411\u91cf\u8fdb\u884c\u6570\u503c\u52a0\u6cd5\uff0c\u5fc5\u987b\u5c06\u5b83\u4eec\u5404\u81ea\u7684\u5206\u91cf\u76f8\u52a0\u3002\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e24\u4e2a\u5411\u91cf\u7684X\u5750\u6807\u76f8\u52a0\u5e76\u4e14\u4e0eY\u5750\u6807\u76f8\u540c\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-d97d089a143f6e30d987b0ed74c56dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} + \\vv{\\text{v}} = (\\text{u}_x + \\text{v}_x \\ , \\ \\text{u}_y + \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u4f60\u53ef\u4ee5\u770b\u5230\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff0c\u6211\u4eec\u5c06\u6dfb\u52a0\u4ee5\u4e0b\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-d5107f1a0b5a49b0ffd79eb20211c48b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (2,3) \\qquad \\vv{\\text{v}}=(4, -1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-24ac65138e4d395f7773aa19ba806a49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} + \\vv{\\text{v}}&amp; =(2,3) +(4,-1) \\\\[2ex] &amp; = (2+4,3+(-1)) \\\\[2ex] &amp; = \\bm{(6,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u5411\u91cf\u4e5f\u53ef\u4ee5\u4ece\u5b83\u4eec\u7684\u56fe\u5f62\u8868\u793a\u4e2d\u76f8\u52a0\u3002\u4e3a\u6b64\uff0c\u901a\u5e38\u4f7f\u7528\u5e73\u884c\u56db\u8fb9\u5f62\u89c4\u5219\u6216\u5b9a\u5f8b\uff0c\u4f46\u65b9\u6cd5\u6709\u5f88\u591a\u3002\u60a8\u53ef\u4ee5\u5728\u6b64\u5904\u67e5\u770b\u6709\u5173 <a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u4e4b\u548c-\u4ee5\u56fe\u5f62\u65b9\u5f0f\u6570\u503c\u6c42\u89e3-\u793a\u4f8b-\u7ec3\u4e60-\u6dfb\u52a0\/\">\u5982\u4f55\u4ee5\u56fe\u5f62\u65b9\u5f0f\u6dfb\u52a0\u4e24\u4e2a\u5411\u91cf\u7684<\/a>\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"resta-de-vectores\"><\/span>\u77e2\u91cf\u51cf\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8981\u4ee5\u89e3\u6790\u65b9\u5f0f\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\uff0c\u5fc5\u987b\u51cf\u53bb\u5b83\u4eec\u5404\u81ea\u7684\u5206\u91cf\u3002\u5373\u4e24\u4e2a\u5411\u91cf\u7684X\u5750\u6807\u76f8\u51cf\uff0c\u4e0eY\u5750\u6807\u76f8\u540c\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-c755aca302ff1c1b956ca3d91bac1095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} - \\vv{\\text{v}} = (\\text{u}_x - \\text{v}_x \\ , \\ \\text{u}_y - \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u51cf\u53bb\u4ee5\u4e0b\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-0e6976699c55e7cb1372aca76313b056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,1) \\qquad \\vv{\\text{v}}=(2, -4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-5693a8287adebc3a4553358f8a8b0969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} - \\vv{\\text{v}}&amp; =(3,1) -(2,-4) \\\\[2ex] &amp; = (3-2,1-(-4)) \\\\[2ex]&amp; = (3-2,1+4) \\\\[2ex] &amp; = \\bm{(1,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e0e\u52a0\u6cd5\u4e00\u6837\uff0c\u60a8\u4e5f\u53ef\u4ee5\u4f7f\u7528 2 \u4e2a\u5411\u91cf\u7684\u8868\u793a\u5f62\u5f0f\u6765\u51cf\u53bb\u5b83\u4eec\u3002\u4e3a\u6b64\uff0c\u901a\u5e38\u4f7f\u7528\u4e09\u89d2\u6cd5\u5219\u6216\u5b9a\u5f8b\uff0c\u4f46\u6709\u51e0\u79cd\u65b9\u6cd5\u3002\u60a8\u53ef\u4ee5\u901a\u8fc7\u793a\u4f8b\u4ee5\u53ca\u6709\u5173<a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u51cf\u6cd5-\u6570\u5b57\u56fe\u5f62-\u4f8b\u5b50-\u89e3\u51b3\u7ec3\u4e60-\u51cf\u6cd5\/\">\u5982\u4f55\u4ee5\u56fe\u5f62\u65b9\u5f0f\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\u7684<\/a>\u5df2\u89e3\u51b3\u7ec3\u4e60\u6765\u67e5\u770b\u5b83\u4eec\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"modulo-de-un-vector\"><\/span>\u5411\u91cf\u7684\u6a21<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u672c\u9875\u5f00\u5934\u6240\u770b\u5230\u7684\uff0c\u5411\u91cf\u7684\u5927\u5c0f\u5bf9\u5e94\u4e8e\u8be5\u5411\u91cf\u7684\u957f\u5ea6\u3002\u90a3\u4e48\uff0c\u5411\u91cf\u7684\u957f\u5ea6\uff08\u6216\u5927\u5c0f\uff09\u53ef\u4ee5\u6839\u636e\u5176\u5206\u91cf\u6765\u786e\u5b9a\u3002<\/p>\n<p>\u8003\u8651\u4efb\u610f\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>\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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95466c107aed66569925d4b89a3a939b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ \\text{u}_x^2+\\text{u}_y^2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\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-6273ca0b37b024bc5684ec07237607bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-4)\" 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-d78c0f573a5d2db399d099ebc4a3cb85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =\\sqrt{3^2+(-4)^2} = \\sqrt{9+16}=\\sqrt{25} = \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"316\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u867d\u7136\u770b\u8d77\u6765\u5f88\u7b80\u5355\uff0c\u4f46\u786e\u5b9a\u77e2\u91cf\u7684\u5927\u5c0f\u53ef\u80fd\u5f88\u590d\u6742\u3002\u5982\u679c\u60a8\u60f3\u67e5\u770b\u66f4\u591a\u793a\u4f8b\u5e76\u901a\u8fc7<a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u516c\u5f0f\u7684\u6a21\u793a\u4f8b\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u5411\u91cf\u6a21\u5757\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a>\u8fdb\u884c\u7ec3\u4e60\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u8bbf\u95ee\u6b64\u94fe\u63a5\u9875\u9762\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"multiplicacion-de-un-vector-por-un-escalar\"><\/span>\u5411\u91cf\u4e58\u4ee5\u6807\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8981\u4ee5\u6570\u503c\u65b9\u5f0f\u8ba1\u7b97\u5411\u91cf\u4e0e\u6570\u5b57\uff08\u6216\u6807\u91cf\uff09\u7684\u4e58\u79ef\uff0c\u5411\u91cf\u7684\u6bcf\u4e2a\u5206\u91cf\u90fd\u5fc5\u987b\u4e58\u4ee5\u8be5\u6570\u5b57\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-dc2018686141332d7620fe51d93dae8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\\\\[4ex]k\\cdot \\vv{\\text{u}} =(k\\cdot \\text{u}_x \\ , \\ k\\cdot \\text{u}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u4e0b\u9762\u7684\u901a\u7528\u793a\u4f8b\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u5982\u4f55\u4fdd\u6301\u5411\u91cf\u7684\u65b9\u5411\uff0c\u800c\u4e0d\u7ba1\u6807\u91cf\u7684\u7b26\u53f7\u5982\u4f55\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5411\u91cf\u7684\u65b9\u5411\u53d6\u51b3\u4e8e\u5b83\u76f8\u4e58\u7684\u6570\u5b57\u7684\u7b26\u53f7\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\/multiplication-ou-produit-dun-nombre-ou-dun-scalaire-par-un-vecteur.webp\" alt=\"\u6570\u5b57\u6216\u6807\u91cf\u4e0e\u5411\u91cf\u7684\u4e58\u6cd5\u6216\u4e58\u79ef\" class=\"wp-image-283\" width=\"298\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u5982\u4f55\u6c42\u5411\u91cf\u548c\u6570\u5b57\u7684\u4e58\u79ef\u7684\u6570\u503c\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-6c2dd0a37f737f7c82d6da8b971ca0f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} =(3,-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-87282d0a06c534058bd4b64120bdf391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{\\text{u}} =(4 \\cdot 3 \\ , \\ 4 \\cdot (-2)) = \\bm{(12,-8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-escalar\"><\/span>\u6807\u91cf\u79ef<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u70b9\u79ef\u662f\u4e00\u79cd\u5411\u91cf\u8fd0\u7b97\uff0c\u5b83\u5c06\u4e24\u4e2a\u5411\u91cf\u76f8\u4e58\u5e76\u5c06\u5b83\u4eec\u8f6c\u6362\u4e3a\u5b9e\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u516c\u5f0f\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-1f09930024fc5c410889bea53d06982e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle  \\vv{\\text{u}} \\cdot \\vv{\\text{v}} = \\text{u}_x\\cdot \\text{v}_x + \\text{u}_y\\cdot \\text{v}_y \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e0b\u9762\u662f\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u7ed3\u679c\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-7437bf59c08f823d3a9ca8b5f32a3f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,2) \\qquad \\vv{\\text{v}} = (-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-d2a8137101f391be2b197764b8b21223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{aligned} \\vv{\\text{u}} \\cdot \\vv{\\text{v}}&amp;=(4,2)\\cdot (-1,3) \\\\[1.5ex]&amp;=4\\cdot (-1) + 2 \\cdot 3 \\\\[1.5ex] &amp; = -4+6  \\\\[1.5ex] &amp; =\\bm{10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u6b64\u94fe\u63a5\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230 <a href=\"https:\/\/mathority.org\/cn\/\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u6807\u91cf\u79ef-\u5df2\u89e3\u51b3\u7684\u793a\u4f8b\u7ec3\u4e60\/\">\u70b9\u79ef\u7684\u66f4\u591a\u793a\u4f8b<\/a>\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u627e\u5230\u53e6\u4e00\u79cd\u6c42\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u70b9\u79ef\u7684\u65b9\u6cd5\uff0c\u8fd9\u79cd\u7c7b\u578b\u7684\u8fd0\u7b97\u7684\u6027\u8d28\u7528\u5411\u91cf\u548c\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-vectorial\"><\/span>\u77e2\u91cf\u79ef<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u867d\u7136\u5b83\u4eec\u7684\u540d\u79f0\u975e\u5e38\u76f8\u4f3c\uff0c\u4f46\u70b9\u79ef\u548c\u53c9\u79ef\u5374\u5b8c\u5168\u4e0d\u540c\u3002<\/p>\n<p><strong>\u53c9\u79ef<\/strong>\uff0c\u4e5f\u79f0\u4e3a\u53c9\u79ef\uff0c\u662f\u7a7a\u95f4\u4e2d\uff08R3\u4e2d\uff09\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u8fd0\u7b97\uff0c\u5373\u5b83\u4eec\u662f\u4e09\u5750\u6807\u5411\u91cf\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6709\u4efb\u610f\u4e24\u4e2a\u4e09\u7ef4\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>\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u7b49\u4e8e\u4ee5\u4e0b 3\u00d73 \u884c\u5217\u5f0f\u7684\u7ed3\u679c\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-6c85dc2dfb37842b31dea465c8887bc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\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}  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\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>\u5206\u522b\u662fX\u3001Y\u3001Z\u8f74\u65b9\u5411\u7684\u5355\u4f4d\u5411\u91cf\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u6240\u5f97\u5411\u91cf\u7684\u65b9\u5411\u5782\u76f4\u4e8e\u4e24\u4e2a\u76f8\u4e58\u5411\u91cf\u3002<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u731c\u6d4b\u7684\uff0c\u89e3\u51b3\u6b64\u7c7b\u8fd0\u7b97\u6bd4\u4ee5\u524d\u7684\u8fd0\u7b97\u66f4\u56f0\u96be\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u6709\u4e00\u6574\u9875\u8be6\u7ec6\u8bf4\u660e\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u53c9\u79ef\u3002\u56e0\u6b64\uff0c\u5982\u679c\u60a8\u6709\u5174\u8da3\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u8bbf\u95ee\u5e76\u7ec3\u4e60<a href=\"https:\/\/mathority.org\/cn\/\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u4ea4\u53c9\u516c\u5f0f\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u5df2\u6c42\u89e3\u7684\u5411\u91cf\u79ef\u7ec3\u4e60<\/a>\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"producto-mixto\"><\/span>\u6df7\u5408\u4ea7\u54c1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e09\u4e2a\u5411\u91cf\u7684<strong>\u6df7\u5408\u79ef<\/strong>\uff0c\u4e5f\u79f0\u4e3a\u4e09\u91cd\u70b9\u79ef\uff0c\u662f\u4e09\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u8fde\u7eed\u4e58\u6cd5\uff0c\u6d89\u53ca\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u7684\u8fd0\u7b97\uff1a\u70b9\u79ef\u548c\u5411\u91cf\u79ef\u3002\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u8fd0\u7b97\u7684\u7ec4\u5408\u7ed9\u51fa\u4e00\u4e2a\u6807\u91cf\uff08\u5b9e\u6570\uff09\u3002<\/p>\n<p>\u5177\u4f53\u5730\uff0c\u6df7\u5408\u4e58\u79ef\u5305\u62ec\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u7684\u5411\u91cf\u4e58\u79ef\uff0c\u5e76\u4e14\u968f\u540e\u5c06\u6240\u83b7\u5f97\u7684\u7ed3\u679c\u4e0e\u7b2c\u4e09\u5411\u91cf\u76f8\u4e58\u3002\u770b\u4e00\u4e0b\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-20bc6ca73caab65fbe6dafc458258ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.3pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}}) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e0e\u5411\u91cf\u79ef\u4e00\u6837\uff0c\u6c42\u89e3\u5411\u91cf\u4e4b\u95f4\u7684\u6df7\u5408\u79ef\u5e76\u4e0d\u5bb9\u6613\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u770b\u4e00\u4e0b<a href=\"https:\/\/mathority.org\/cn\/\u4e09\u4e2a\u5411\u91cf\u6216\u4e09\u91cd\u6807\u91cf\u79ef\u7684\u6df7\u5408\u79ef\u793a\u4f8b\/\">\u4e09\u4e2a\u5411\u91cf\u7684\u6df7\u5408\u4e58\u79ef<\/a>\u7684\u89e3\u91ca\uff0c\u60a8\u5c06\u5728\u5176\u4e2d\u627e\u5230\u793a\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4ee5\u53ca\u8be5\u5411\u91cf\u8fd0\u7b97\u7684\u51e0\u4f55\u610f\u4e49\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-vectores\"><\/span>\u5411\u91cf\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5411\u91cf\u6709\u8bb8\u591a\u4e0d\u540c\u7c7b\u578b\uff0c\u4f46\u9700\u8981\u4e86\u89e3\u7684\u6700\u91cd\u8981\u7684\u5b9a\u4e49\u662f\uff1a<\/p>\n<ul>\n<li><strong>\u5355\u4f4d\u5411\u91cf<\/strong>\uff1a\u6a21\u7b49\u4e8e1\u7684\u5411\u91cf\u3002<\/li>\n<li><strong>\u56fa\u5b9a\u5411\u91cf<\/strong>\uff1a\u5f53\u5411\u91cf\u7684\u539f\u70b9\u5e94\u7528\u4e8e\u56fa\u5b9a\u70b9\u65f6\uff0c\u5411\u91cf\u662f\u56fa\u5b9a\u7684\u3002<\/li>\n<li><strong>\u81ea\u7531\u5411\u91cf<\/strong>\uff1a\u5f53\u5411\u91cf\u7684\u4f5c\u7528\u70b9\u672a\u5b9a\u4e49\u4f46\u4e3a\u81ea\u7531\u70b9\u65f6\uff0c\u5411\u91cf\u662f\u81ea\u7531\u7684\u3002<\/li>\n<li><strong>\u5171\u7ebf\u5411\u91cf<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u5171\u4eab\u76f8\u540c\u7684\u4f5c\u7528\u7ebf\uff08\u5411\u91cf\u6240\u5728\u7684\u7ebf\uff09\uff0c\u5219\u5b83\u4eec\u662f\u5171\u7ebf\u7684\u3002<\/li>\n<li><strong>\u7b49\u4ef7\u5411\u91cf<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u5927\u5c0f\u3001\u76f8\u540c\u7684\u610f\u4e49\u548c\u76f8\u540c\u7684\u65b9\u5411\uff0c\u5219\u5b83\u4eec\u662f\u7b49\u4ef7\u7684\uff08\u5c3d\u7ba1\u5b83\u4eec\u53ef\u4ee5\u6709\u4e0d\u540c\u7684\u5e94\u7528\u70b9\uff09\u3002<\/li>\n<li><strong>\u94fe\u63a5\u5411\u91cf<\/strong>\uff1a\u94fe\u63a5\u5411\u91cf\u662f\u4e5f\u4f5c\u7528\u4e8e\u540c\u4e00\u76f4\u7ebf\u7684\u7b49\u82b1\u7c89\u5411\u91cf\u3002<\/li>\n<li><strong>\u76f8\u53cd\u5411\u91cf<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u5927\u5c0f\u548c\u76f8\u540c\u7684\u65b9\u5411\u4f46\u65b9\u5411\u4e0d\u540c\uff0c\u5219\u5b83\u4eec\u76f8\u53cd\u3002<\/li>\n<li><strong>\u4f4d\u7f6e\u5411\u91cf<\/strong>\uff1a\u4f4d\u7f6e\u5411\u91cf\u662f\u4ee5\u70b9(0,0)\uff08\u5750\u6807\u539f\u70b9\uff09\u4e3a\u539f\u70b9\u7684\u5411\u91cf\u3002<\/li>\n<li><strong>\u7ade\u4e89\u5411\u91cf<\/strong>\uff1a\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u7684\u4f5c\u7528\u7ebf\u7ecf\u8fc7\u540c\u4e00\u70b9\uff08\u5373\u76f8\u4ea4\uff09\u65f6\uff0c\u5b83\u4eec\u662f\u5e76\u53d1\u7684\u3002<\/li>\n<li><strong>\u5e73\u884c\u5411\u91cf<\/strong>\uff1a\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u5982\u679c\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\uff0c\u5219\u65e0\u8bba\u5176\u65b9\u5411\u5982\u4f55\uff0c\u5b83\u4eec\u90fd\u662f\u5e73\u884c\u7684\u3002<\/li>\n<li><strong>\u5782\u76f4\u5411\u91cf<\/strong>\uff1a\u5f53\u4e24\u4e2a\u5411\u91cf\u7684\u65b9\u5411\u5f62\u6210 90\u00b0 \u89d2\u65f6\uff0c\u5b83\u4eec\u662f\u5782\u76f4\uff08\u6216\u6b63\u4ea4\uff09\u7684\u3002<\/li>\n<li><strong>\u6b63\u4ea4\u5411\u91cf<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u5f7c\u6b64\u5782\u76f4\uff0c\u5e76\u4e14\u5b83\u4eec\u662f\u5e7a\u6b63\u7684\uff08\u5b83\u4eec\u7684\u5927\u5c0f\u7b49\u4e8e 1\uff09\uff0c\u5219\u5b83\u4eec\u662f\u6b63\u4ea4\u5411\u91cf\u3002<\/li>\n<li><strong>\u5171\u9762\u5411\u91cf<\/strong>\uff1a\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\u65f6\u662f\u5171\u9762\u7684\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"angulo-entre-dos-vectores\"><\/span>\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u627e\u5230\u4e24\u4e2a\u7ed9\u5b9a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\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-67007d32353dedf96eb6b965b16c5489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\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-4501274336c637b37c6332eae5c6c229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -5px;\"><\/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>\u662f\u5411\u91cf\u7684\u6a21<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" 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-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5206\u522b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5411\u91cf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u4eec\u662f\u4ec0\u4e48\u3001\u5b83\u4eec\u7684\u7279\u5f81\u3001\u5b83\u4eec\u5982\u4f55\u8ba1\u7b97\u3001\u5982\u4f55\u5bf9\u5411\u91cf\u8fdb\u884c\u8fd0\u7b97\u3001\u5b58\u5728\u7684\u4e0d\u540c\u7c7b &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%bb%80%e4%b9%88%e6%98%af%e5%90%91%e9%87%8f-%e6%95%b0%e5%ad%a6-%e7%89%a9%e7%90%86-%e4%be%8b%e5%ad%90\/\"> <span class=\"screen-reader-text\">\u4ec0\u4e48\u662f\u5411\u91cf\uff08\u6570\u5b66\uff09\uff1f<\/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-268","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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