{"id":270,"date":"2023-07-10T01:20:15","date_gmt":"2023-07-10T01:20:15","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e5%92%8c%e5%b9%b3%e9%9d%a2%e4%b9%8b%e9%97%b4%e7%9a%84%e8%a7%92%e5%ba%a6%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T01:20:15","modified_gmt":"2023-07-10T01:20:15","slug":"%e7%9b%b4%e7%ba%bf%e5%92%8c%e5%b9%b3%e9%9d%a2%e4%b9%8b%e9%97%b4%e7%9a%84%e8%a7%92%e5%ba%a6%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e5%92%8c%e5%b9%b3%e9%9d%a2%e4%b9%8b%e9%97%b4%e7%9a%84%e8%a7%92%e5%ba%a6%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u60a8\u8fd8\u53ef\u4ee5\u67e5\u770b\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-el-angulo-entre-una-recta-y-un-plano\"><\/span>\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u662f\u76f4\u7ebf\u4e0e\u5176\u5728\u5e73\u9762\u4e0a\u7684\u6b63\u4ea4\u6295\u5f71\u4e4b\u95f4\u7684\u5939\u89d2\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\/angle-entre-une-ligne-et-un-plan.webp\" alt=\"\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u591a\u5c11\uff1f\" class=\"wp-image-3943\" width=\"500\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u76f4\u7ebf\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u8be5\u76f4\u7ebf\u4e0e\u5782\u76f4\u4e8e\u8be5\u5e73\u9762\u7684\u77e2\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u8865\u89d2\u3002\u56e0\u6b64\uff0c\u76f4\u7ebf\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u6839\u636e\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u4e0e\u5e73\u9762\u7684\u6cd5\u7ebf\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u6765\u8ba1\u7b97\u7684\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-una-recta-y-un-plano\"><\/span>\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u63a8\u5bfc\u5e73\u9762\u548c\u76f4\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f\uff0c\u60a8\u9700\u8981\u77e5\u9053\u5982\u4f55<a href=\"https:\/\/mathority.org\/cn\/\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u627e\u5230\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6<\/a>\u3002\u5728\u94fe\u63a5\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u8bf4\u660e\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u60a8\u4e0d\u8bb0\u5f97\u5982\u4f55\u64cd\u4f5c\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u770b\u4e00\u4e0b\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u4e0e\u6240\u8ff0\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u4e92\u8865<\/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-e01bc8353ce87c4e409251c9a78dae8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}_r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"29\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4ee5\u53ca\u8be5\u5e73\u9762\u7684\u6cd5\u5411\u77e2\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45cf5bc44c73892962f2e851f74daacc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{n})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff0c\u4ece\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f\u6211\u4eec\u63a8\u5bfc\u51fa\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u76f8\u5f53\u4e8e\u4ee5\u4e0b\u8868\u8fbe\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-432b11c5cc73074467112392e29b46ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)=\\cos(90-\\alpha) =\\cfrac{\\lvert \\vv{\\text{v}}_r \\cdot \\vv{n} \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"247\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u76f4\u7ebf\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u5939\u89d2\u516c\u5f0f\u4e3a<\/strong>\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-entre-une-droite-et-un-plan-formule.webp\" alt=\"\u76f4\u7ebf\u4e0e\u516c\u5f0f\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\" class=\"wp-image-3975\" width=\"282\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50f32076ae1ee85f5b7c5a6d43a03089_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u76f4\u7ebf\u7684\u76f4\u5411\u91cf\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10affe1faee06a5faa4ef6d9c0473b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u5411\u91cf\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-angulo-entre-una-recta-y-un-plano\"><\/span>\u8ba1\u7b97\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5982\u4f55\u89e3\u51b3\u6b64\u7c7b\u95ee\u9898\uff0c\u4e0b\u9762\u662f\u8ba1\u7b97\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u76f4\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6\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>\u4e0e\u98de\u673a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8bbe\u4ed6\u4eec\u7684\u65b9\u7a0b\u4e3a\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-cb8b61cb99a7af826a63ee098efc3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x= 3-t \\\\[1.7ex] y = 2+4t \\\\[1.7ex] z=-3t \\end{cases}\\qquad\\qquad \\pi : \\ x-y+4z+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"392\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8be5\u76f4\u7ebf\u4ee5\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u6545\u5176\u65b9\u5411\u5411\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-f5c132cae76c4e7d2eef34b80dda60e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-1,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5e73\u9762\u4ee5\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u56e0\u6b64\u5176\u6cd5\u5411\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-6c8001623f05fee4f3266c426e184482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (1,-1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u548c\u5e73\u9762\u7684\u6cd5\u7ebf\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5e94\u7528\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u5411\u91cf\u4ee3\u5165\u516c\u5f0f\u4e2d\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-60faf9957c871b9c9e62fe4ffc9b6973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-1,4,-3) \\cdot (1,-1,4)\\rvert}{\\sqrt{(-1)^2+4^2+(-3)^2} \\cdot \\sqrt{1^2+(-1)^2+4^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"393\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8fdb\u884c\u8ba1\u7b97\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-ecf6e128745b2cea94a0651a086d9708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -1\\cdot 1 +4 \\cdot (-1) + (-3) \\cdot 4\\rvert}{\\sqrt{26}\\cdot \\sqrt{18}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"289\" style=\"vertical-align: -16px;\"><\/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-d9ddce2ff5d93699f7583e541c33126d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-17|}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"125\" style=\"vertical-align: -16px;\"><\/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-df350eb37802b9a0fd712299478ece35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{17}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"117\" style=\"vertical-align: -16px;\"><\/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-77b7a2aaf4989013b48a34274af4b246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,79\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u7528\u8ba1\u7b97\u5668\u53cd\u8f6c\u6b63\u5f26\u503c\u5e76\u627e\u5230\u89d2\u5ea6\u503c\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-4222f5a3e1dc32c123215c725dffadcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,79) = \\bm{51,80\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7ea6\u4e3a 51.80\u00b0\u3002<\/p>\n<p>\u6211\u4eec\u5fc5\u987b\u8003\u8651\u5230\uff0c\u5982\u679c\u6211\u4eec\u5f97\u5230 0\u00b0 \u7684\u7ed3\u679c\uff0c\u8fd9\u610f\u5473\u7740\u76f4\u7ebf\u548c\u5e73\u9762\u5e73\u884c\u6216\u8005\u76f4\u7ebf\u5305\u542b\u5728\u5e73\u9762\u5185\u3002\u5982\u679c\u89d2\u5ea6\u7b49\u4e8e 90\u00b0\uff0c\u5219\u610f\u5473\u7740\u76f4\u7ebf\u548c\u5e73\u9762\u5782\u76f4\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-angulo-entre-una-recta-y-un-plano\"><\/span>\u89e3\u51b3\u4e86\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u627e\u51fa\u76f4\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6<\/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>\u4e0e\u98de\u673a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8bbe\u4ed6\u4eec\u7684\u65b9\u7a0b\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-187a958fc02bef31b18b2c2f95379015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\cfrac{x-1}{2} = \\cfrac{y+1}{-1} = \\cfrac{z+3}{-3}\" 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-97968f3ad3bc2327d83f308575a4607d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 3x+y+2z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"184\" style=\"vertical-align: -4px;\"><\/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\">\u76f4\u7ebf\u8868\u793a\u4e3a\u8fde\u7eed\u65b9\u7a0b\uff0c\u6545\u5176\u65b9\u5411\u5411\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-ce8d892f9706e946ee38bea5601f420c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (2,-1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5e73\u9762\u662f\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u56e0\u6b64\u5176\u6cd5\u5411\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-d9b2fb6c5a45dd5cff0e5c949ab7ee22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u548c\u5e73\u9762\u7684\u6cd5\u7ebf\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-f79b0514974ecd648d402afe09fce215_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(2,-1,-3) \\cdot (3,1,2)\\rvert}{\\sqrt{2^2+(-1)^2+(-3)^2} \\cdot \\sqrt{3^2+1^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"362\" style=\"vertical-align: -20px;\"><\/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-43b3452fc0559594f81d5793eb69bd50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert 2\\cdot 3 +(-1) \\cdot 1 + (-3) \\cdot 2\\rvert}{\\sqrt{14}\\cdot \\sqrt{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"275\" style=\"vertical-align: -16px;\"><\/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-0fae771d5c74fc70f8c235e7d977b97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-1|}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"116\" 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-4af96594105dfe56eb0b48a782596cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{1}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" 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-c26a8cbca5ca49005ddf750822a16359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,07\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u53cd\u8f6c\u6b63\u5f26\u5e76\u627e\u5230\u89d2\u5ea6\u503c\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-6280b70e3e9db10239c8ed41338921b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,07) = \\bm{4,10\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u4e3a4.10\u00b0\u3002<\/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>\u786e\u5b9a\u76f4\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6<\/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>\u4e0e\u98de\u673a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8bbe\u4ed6\u4eec\u7684\u65b9\u7a0b\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-6a8165b8e50fbc7764c77d1a984de353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} 3x-y+4z+1=0 \\\\[2ex] x+2y-2z+6=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"198\" 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-4ef4dec995f97607a7e037e37eeb0b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ -4x+2y-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"167\" style=\"vertical-align: -4px;\"><\/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\">\u76f4\u7ebf\u7528\u5176\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u8868\u793a\uff0c\u56e0\u6b64\u9700\u8981\u901a\u8fc7\u8ba1\u7b97\u5782\u76f4\u4e8e\u786e\u5b9a\u76f4\u7ebf\u7684 2 \u4e2a\u5e73\u9762\u7684\u5411\u91cf\u7684\u5411\u91cf\u79ef\u6765\u627e\u5230\u76f4\u7ebf\u7684\u65b9\u5411\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-54cc86087728e7e163034c95afc55286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -1 &amp; 4 \\\\[1.1ex] 1 &amp;2&amp;-2 \\end{vmatrix}  = -6\\vv{i}+10\\vv{j}+7\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"236\" 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-d96017e2fa07a08307c10dc57ee61c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-6,10,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u77e2\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-029b4c2fd253e26ab1b4c273507b5527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (-4,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u548c\u5e73\u9762\u7684\u6cd5\u7ebf\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-dc066db1739212edabe5d565f906830b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-6,10,7) \\cdot (-4,2,0)\\rvert}{\\sqrt{(-6)^2+10^2+7^2} \\cdot \\sqrt{(-4)^2+2^2+0^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"374\" style=\"vertical-align: -20px;\"><\/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-d143bdbebf8285d4543063a31d886c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -6\\cdot (-4) +10 \\cdot 2 + 7 \\cdot 0\\rvert}{\\sqrt{185}\\cdot \\sqrt{20}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"271\" style=\"vertical-align: -16px;\"><\/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-35ceee51406f9d5bcc316b74690eb299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{44}{\\sqrt{3700}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"126\" style=\"vertical-align: -16px;\"><\/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-84549d70edc1d856e90c75ec50421389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,72\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u53cd\u8f6c\u6b63\u5f26\u5e76\u627e\u5230\u89d2\u5ea6\u503c\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-e843d4cbca4933f7ba383adcd6566028_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,72) = \\bm{46,33\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u4e3a46.33\u00b0\u3002<\/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>\u4f7f\u7528\u76f4\u7ebf\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f\u6c42\u51fa<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u6743\u5229\u6240\u5fc5\u9700\u7684<\/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>\u548c\u98de\u673a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5e73\u884c\u7684\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-5ce940060c57c2eae41e79fb31db1afe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ (x,y,z) = (2,0-1)+t(4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" 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-2f733e6dda28d7a2ab79930a2e311d76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 4x+3y+kz+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"194\" style=\"vertical-align: -4px;\"><\/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\u5c06\u76f4\u7ebf\u8868\u793a\u4e3a\u5411\u91cf\u65b9\u7a0b\uff0c\u6545\u5176\u65b9\u5411\u5411\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-d80ac01e619cde85001850e17e3f2bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5e73\u9762\u662f\u4e00\u822c\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u5b83\u7684\u6cd5\u5411\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-b4a7ab8f96745e213fbc290625f5b463_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e3a\u4e86\u4f7f\u4e24\u4e2a\u51e0\u4f55\u5143\u7d20\u5e73\u884c\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684\u89d2\u5ea6\u5fc5\u987b\u4e3a\u96f6\u3002\u56e0\u6b64\uff0c\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5939\u89d2\u516c\u5f0f\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-efc7281925b7c514913e4aaf9102d342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(0\u00ba) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"133\" style=\"vertical-align: -17px;\"><\/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-240cba5c3a27806488b1e8172b55b8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" style=\"vertical-align: -17px;\"><\/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-61e18ce576fafff8b4db05f6bca9cedb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert =\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" 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-4639b105473c348e32b6d87593e0ab31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\vv{\\text{v}}_r \\cdot \\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u548c\u6cd5\u7ebf\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u5fc5\u987b\u4e3a\u96f6\u3002\u4ece\u8fd9\u4e2a\u65b9\u7a0b\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u672a\u77e5\u6570\u7684\u503c<\/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-7cf6d2c84f82625cb8a795ee1394251f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" 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-7dd4a6abbc2ab11fe54f43b6aeea5ee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(4,-1,3) \\cdot (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" 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-ecedbfc73f2ae09aa2f20d886b76217a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =4\\cdot 4 -1\\cdot 3 +3 \\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"168\" style=\"vertical-align: -2px;\"><\/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-d6b2fc367d696e22656777d9c8394f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =16 -3 +3 k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"120\" style=\"vertical-align: -2px;\"><\/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-14bd0daaa168493c0978bdec5f548829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -3k =13\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-27a35752a178021d706238eff36fe7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k =\\cfrac{13}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" 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-0aef8d9f84e0eeb1eceb52873846ca57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =-}\\mathbf{\\cfrac{13}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u6700\u540e\uff0c\u5982\u679c\u60a8\u53d1\u73b0\u672c\u6587\u6709\u5e2e\u52a9\uff0c\u60a8\u53ef\u80fd\u4e5f\u5bf9\u5982\u4f55\u627e\u5230<a href=\"https:\/\/mathority.org\/cn\/\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f-r3\/\">\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6<\/a>\u611f\u5174\u8da3\u3002\u5728\u94fe\u63a5\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u975e\u5e38\u8be6\u7ec6\u7684\u89e3\u91ca\u4ee5\u53ca\u8ba1\u7b97\u4e24\u4e2a\u4e0d\u540c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u6240\u9700\u7684\u516c\u5f0f\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u80fd\u591f\u7ec3\u4e60\u548c\u7406\u89e3\u5b83\u662f\u5982\u4f55\u5b8c\u7f8e\u5b8c\u6210\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u60a8\u8fd8\u53ef\u4ee5\u67e5\u770b\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e5%92%8c%e5%b9%b3%e9%9d%a2%e4%b9%8b%e9%97%b4%e7%9a%84%e8%a7%92%e5%ba%a6%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u76f4\u7ebf\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6<\/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":[15],"tags":[],"class_list":["post-270","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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