{"id":227,"date":"2023-07-10T22:13:46","date_gmt":"2023-07-10T22:13:46","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e6%9d%a1%e7%ba%bf%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%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0%e6%96%9c%e7%8e%87%e5%af%bc%e6%bc%94%e5%90%91\/"},"modified":"2023-07-10T22:13:46","modified_gmt":"2023-07-10T22:13:46","slug":"%e4%b8%a4%e6%9d%a1%e7%ba%bf%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%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0%e6%96%9c%e7%8e%87%e5%af%bc%e6%bc%94%e5%90%91","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e6%9d%a1%e7%ba%bf%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%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0%e6%96%9c%e7%8e%87%e5%af%bc%e6%bc%94%e5%90%91\/","title":{"rendered":"\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff08\u516c\u5f0f\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5982\u4f55\u8ba1\u7b97\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff08\u516c\u5f0f\uff09\u7684\u8bf4\u660e\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\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-es-el-angulo-entre-dos-rectas\"><\/span>\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u591a\u5c11\uff1f <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-105\"><\/div>\n<\/div>\n<p><strong>\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u8fd9\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u6700\u5c0f\u89d2\u5ea6\u3002<\/strong> <\/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-deux-lignes-1.webp\" alt=\"\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\" class=\"wp-image-1637\" width=\"225\" height=\"206\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5728\u5e73\u9762\u56fe\u4e2d\uff0c\u6839\u636e\u7ebf\u4e4b\u95f4\u5f62\u6210\u7684\u89d2\u5ea6\uff0c\u6709\u56db\u79cd\u7c7b\u578b\u7684\u7ebf\uff1a\u76f8\u4ea4\u7ebf\uff080\u00b0 \u5230 90\u00b0 \u4e4b\u95f4\uff09\u3001\u5782\u76f4\u7ebf\uff0890\u00b0\uff09\u3001\u5e73\u884c\u7ebf\uff080\u00b0\uff09\u548c\u91cd\u5408\u7ebf\uff080\u00b0\uff09\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-143\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u76f8\u4ea4\u7ebf<\/strong><\/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\/angles-droits-secants.webp\" alt=\"\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\" class=\"wp-image-1644\" width=\"205\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u76f8\u4ea4\u7ebf\u4ee5 0\u00b0 \u5230 90\u00b0 \u4e4b\u95f4\u7684\u9510\u89d2\u76f8\u4ea4\u3002 <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong><strong>\u5782\u76f4\u76f4\u7ebf<\/strong><\/strong><\/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-perpendiculaires-a-90-degres.webp\" alt=\"\u4e24\u6761\u5782\u76f4\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\" class=\"wp-image-1884\" width=\"181\" height=\"207\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5782\u76f4\u7ebf\u76f8\u4ea4\u6210 90\u00b0 \u76f4\u89d2\u3002 <\/p>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<div class=\"wp-block-columns is-layout-flex wp-container-146\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u5e73\u884c\u7ebf<\/strong><\/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\/droites-paralleles-a-langle.webp\" alt=\"\" class=\"wp-image-1643\" width=\"217\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5e73\u884c\u7ebf\u6c38\u8fdc\u4e0d\u4f1a\u76f8\u4ea4\u5e76\u4e14\u5b83\u4eec\u4e4b\u95f4\u7684\u89d2\u5ea6\u4e3a 0\u00b0\u3002 <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u91cd\u5408\u7ebf<\/strong><\/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-coincident-lignes.webp\" alt=\"\" class=\"wp-image-1646\" width=\"189\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4e24\u6761\u91cd\u5408\u7ebf\u5177\u6709\u6240\u6709\u516c\u5171\u70b9\uff0c\u56e0\u6b64\u5b83\u4eec\u4e4b\u95f4\u59cb\u7ec8\u5b58\u5728 0\u00b0 \u89d2\u5ea6\u3002<\/p>\n<\/div>\n<\/div>\n<p>\u603b\u4e4b\uff0c\u4e24\u6761\u5e73\u884c\u7ebf\u3001\u91cd\u5408\u7ebf\u6216\u5782\u76f4\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u8ba1\u7b97\u662f\u7acb\u5373\u7684\uff1a\u5e73\u884c\u7ebf\u548c\u91cd\u5408\u7ebf\u7531\u4e8e\u65b9\u5411\u76f8\u540c\u800c\u5f62\u6210 0 \u5ea6\u7684\u89d2\u5ea6\uff0c\u5782\u76f4\u7ebf\u76f8\u4ea4\u7684\u89d2\u5ea6\u4e3a 90 \u5ea6\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u8981\u627e\u5230\u4e24\u6761\u76f8\u4ea4\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u60a8\u5fc5\u987b\u5e94\u7528\u516c\u5f0f\uff08\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u770b\u5230\uff09\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-el-angulo-entre-dos-rectas\"><\/span>\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1f <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\u4e24\u79cd\u65b9\u6cd5\u53ef\u4ee5\u8ba1\u7b97\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u7b2c\u4e00\u79cd\u65b9\u6cd5\u4f7f\u7528\u6bcf\u6761\u7ebf\u7684<strong>\u65b9\u5411\u5411\u91cf<\/strong>\uff0c\u7b2c\u4e8c\u79cd\u65b9\u6cd5\u57fa\u4e8e\u6bcf\u6761\u7ebf\u7684<strong>\u659c\u7387<\/strong>\u3002<\/p>\n<p>\u8fd9\u4e24\u79cd\u65b9\u6cd5\u90fd\u4e0d\u6bd4\u53e6\u4e00\u79cd\u66f4\u597d\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u4e24\u79cd\u65b9\u6cd5\u90fd\u975e\u5e38\u7b80\u5355\uff0c\u4f46\u6839\u636e\u7ebf\u6761\u7684\u8868\u8fbe\u65b9\u5f0f\uff0c\u4e00\u79cd\u65b9\u6cd5\u6216\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u5426\u5b9e\u7528\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u4e86\u89e3\u5982\u4f55\u4f7f\u7528\u8fd9\u4e24\u79cd\u6570\u5b66\u65b9\u6cd5\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"metodo-de-los-vectores-directores-de-las-rectas\"><\/span>\u7ebf\u77e2\u91cf\u5b9a\u5411\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4f7f\u7528\u65b9\u5411\u5411\u91cf\u8ba1\u7b97\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u516c\u5f0f\u4e3a\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u7ed9\u5b9a\u4e24\u6761\u4e0d\u540c\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-b626c82ac04d69ba3bcafb5fa87d7d00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\\qquad \\vv{\\text{v}} = (\\text{v}_x,\\text{v}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"216\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u8fd9\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u53ef\u4ee5\u7528\u4ee5\u4e0b\u516c\u5f0f\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-19eb97a6cf27fffc3ea832e388f924a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{\\text{u}} \\cdot \\vv{\\text{v}}\\rvert}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"127\" 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-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<\/div>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u77e2\u91cf\u5927\u5c0f\u7684\u516c\u5f0f\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0761a6a31d273eefccceb4aad7556a6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{v}} \\rvert = \\sqrt{ \\text{v}_x^2+\\text{v}_y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"117\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\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-a336a6cbbd7581f1fb6481561aef1efc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=2-3t \\\\[2ex]y=1+4t \\end{cases} \\qquad s: \\ 2x-5y+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"334\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u8981\u8ba1\u7b97\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u5fc5\u987b\u9996\u5148\u627e\u5230\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u3002<\/p>\n<p>\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>\u4ee5<a href=\"https:\/\/mathority.org\/cn\/\u76f4\u7ebf\u53c2\u6570\u65b9\u7a0b\u7684\u516c\u5f0f\/\">\u53c2\u6570\u65b9\u7a0b<\/a>\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u56e0\u6b64\u6807\u8bb0\u5176\u65b9\u5411\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-5d3e98a6c4a49b9b38e463795eb44b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-3,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u548c\u6cd5\u5f8b<\/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-ea93feaa2c7157ec666d9a59c0f6a699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4ee5\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u56e0\u6b64\u5176\u65b9\u5411\u5411\u91cf\u7684\u5750\u6807\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-25fa1b333fb55fd35e2ff773a99aab2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (-B,A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" 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-59f221044ed855cbee5120d8936cc247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e24\u6761\u7ebf\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u786e\u5b9a\u4e24\u4e2a\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-5630e1894a54b931779a240cce2b3460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{(-3)^2+4^2}= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"172\" 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-3b8dca924b988372d9cc00e5a3e79041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{5^2+2^2}= \\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5bf9\u89d2\u5ea6\u516c\u5f0f\u8fdb\u884c\u5411\u91cf\u8fd0\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" 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-1f1810380fc6ddab753a49fb43d8d136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(-3,4) \\cdot (5,2)\\rvert}{5 \\cdot \\sqrt{29}}= \\cfrac{\\lvert-3 \\cdot 5 + 4\\cdot 2\\rvert}{26,93} = \\cfrac{7}{26,93} = 0,26\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"449\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u7528\u4f59\u5f26\u7684\u5012\u6570\u8ba1\u7b97\u4e24\u6761\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-839ce1333f41e5392ef7d2127853aae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,26) = \\bm{74,93\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5e26\u6709 \u952e\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u4f59\u5f26\u7684\u5012\u6570<\/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-8b70d14d21b828bcf46c4104f901c916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{\\cos ^{-1}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"57\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"metodo-de-las-pendientes\"><\/span>\u659c\u7387\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u663e\u7136\uff0c\u8981\u7406\u89e3\u8fd9\u79cd\u65b9\u6cd5\uff0c\u60a8\u9700\u8981\u77e5\u9053<a href=\"https:\/\/mathority.org\/cn\/\u76f4\u7ebf\u659c\u7387\u516c\u5f0f\/\">\u76f4\u7ebf\u7684\u659c\u7387<\/a>\u3002\u60a8\u53ef\u4ee5\u5728\u94fe\u63a5\u4e2d\u56de\u987e\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5728\u8fd9\u91cc\u60a8\u53ef\u4ee5\u627e\u5230\u5b83\u7684\u542b\u4e49\u3001\u8ba1\u7b97\u65b9\u5f0f\u3001\u76f4\u7ebf\u659c\u7387\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u7684\u8be6\u7ec6\u89e3\u91ca\u3002<\/p>\n<p>\u6839\u636e\u4e24\u6761\u76f4\u7ebf\u7684\u659c\u7387\u8ba1\u7b97\u5176\u5939\u89d2\u7684\u516c\u5f0f\u4e3a\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u6216\u8005\u4e24\u6761\u4e0d\u540c\u7684\u7ebf\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-a9768adb30eaa8e08b67c58e5c4921df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_1 : \\ y=m_1 x+n_1 \\qquad r_2: \\ y=m_2 x+n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"321\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u8fd9\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u786e\u5b9a\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-82acfc9ae51ee3a469cfabc7024aa75c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_2-m_1}{1+m_1\\cdot m_2} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"166\" 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-51921237944fd6e43f0640228a37376f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"22\" style=\"vertical-align: -3px;\"><\/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-f6dae86895dac0d4644151786b47c7ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u7ebf\u7684\u659c\u7387<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ce00e1b287bac058a29aa4a5cc2b715_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/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-80681c4f8159fb897fed760530a2ef01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u5206\u522b\u3002<\/p>\n<\/div>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u4f7f\u7528\u4e24\u6761\u7ebf\u7684\u659c\u7387\u6765\u8ba1\u7b97\u5b83\u4eec\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a<\/p>\n<ul>\n<li>\u6c42\u4e0b\u5217\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\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-37af9568ead27bf5cc0bedd4e23107b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=4x-2 \\qquad s: \\ y=-3x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"272\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6bcf\u6761\u7ebf\u7684\u659c\u7387\u662f\u53d8\u91cf\u4e4b\u524d\u7684\u6570\u5b57<\/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-845f2902b8bebf60c3c7372a7fbe4d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-6fd143f62c08661d4c17431b128bdcf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\"><\/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-a6063973129bb0bac4b98714e474f8ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_s = -3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u659c\u7387\u516c\u5f0f\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" 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-639af21616a579864711c6c3466a5157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{-3-4}{1+4\\cdot (-3)} \\end{vmatrix}=\\begin{vmatrix} \\cfrac{-7}{-11} \\end{vmatrix} = 0,64\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"294\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\u6211\u4eec\u627e\u5230\u5207\u7ebf\u7684\u5012\u6570\u7684\u89d2\u5ea6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-caed83d6028d223b06c41f639e5323e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{tg}^{-1}(0,64) = \\bm{32,62\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5e26\u6709 \u952e\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u6b63\u5207\u7684\u5012\u6570<\/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-2be52d0cf4b9ef4f831429feec90b416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{\\tan ^{-1}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"59\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u4e00\u4e2a\u793a\u4f8b\uff0c\u5176\u4e2d\u4e24\u6761\u76f4\u7ebf\u7684\u659c\u7387\u8868\u793a\u4e3a\u663e\u5f0f\u65b9\u7a0b\uff0c\u4f46\u5982\u679c\u5b83\u4eec\u91c7\u7528<a href=\"https:\/\/mathority.org\/cn\/\u65b9\u7a0b\u70b9\u76f4\u7ebf\u659c\u7387\u516c\u5f0f\/\">\u70b9\u659c\u7387\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c<\/a>\u5219\u5fc5\u987b\u4f7f\u7528\u76f8\u540c\u7684\u8fc7\u7a0b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-angulos-entre-dos-rectas\"><\/span>\u89e3\u51b3\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u4e0b\u5217\u4e24\u6761\u76f4\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-975bcacc5eecede0a2288a39eeb27a73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=4+t \\\\[2ex]y=-3-2t \\end{cases} \\qquad s: \\ \\begin{cases} x=4t \\\\[2ex]y=-1-t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"324\" style=\"vertical-align: 0px;\"><\/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\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u65b9\u5411\u5411\u91cf\u65b9\u6cd5\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u6c42\u51fa\u6bcf\u6761\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u3002\u4e24\u6761\u7ebf\u90fd\u8868\u793a\u4e3a\u53c2\u6570\u65b9\u7a0b\uff0c\u56e0\u6b64\u5b83\u4eec\u7684\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u5c31\u662f\u53c2\u6570\u524d\u9762\u7684\u9879<\/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-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" 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-ac0191cf7cbec493c10a4fa8197e2a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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-97225ee00d3957d5d85cdc93c8015ed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e24\u6761\u7ebf\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6211\u4eec\u786e\u5b9a\u4e24\u4e2a\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-2e501df610a9ae606c598ec472017f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{1^2+(-2)^2}= \\sqrt{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"187\" 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-b9e23805a7bdb58bd0b4893d4b6e586a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{4^2+(-1)^2}= \\sqrt{17}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u5206\u5b50\u7684\u4e24\u4e2a\u5411\u91cf\u4e0e\u5206\u6bcd\u7684\u6a21\u7684\u4e58\u6cd5\u4e4b\u95f4\u7684\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" 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-e5d926125129db13c541515e1dd0beba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(1,-2) \\cdot (4,-1)\\rvert}{\\sqrt{5} \\cdot \\sqrt{17}}= \\cfrac{\\lvert 1 \\cdot 4 + (-2)\\cdot (-1)\\rvert}{9,22} = \\cfrac{6}{9,22} = 0,65\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"494\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u4f59\u5f26\u7684\u5012\u6570\u627e\u5230\u4e24\u6761\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ede88ebdcf81c8914fed546ba2a0d1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,65) = \\bm{49,40\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u6c42\u4e0b\u5217\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-818fae5a2074424ec782243f26c5708c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ -3x+4y+1=0 \\qquad s: \\ \\cfrac{x-1}{6} = \\cfrac{y+5}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"337\" 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\">\u6211\u4eec\u5c06\u4f7f\u7528\u65b9\u5411\u5411\u91cf\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6240\u4ee5\u9996\u5148\u6211\u4eec\u9700\u8981\u627e\u5230\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\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>\u4ee5\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u4f7f\u5f97\u6807\u8bb0\u5176\u65b9\u5411\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-381327f58ef6c881ed34e78624c91b8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-B,A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" 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-383a5264ab7ded87d5684560e6263e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u548c\u6cd5\u5f8b<\/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-ea93feaa2c7157ec666d9a59c0f6a699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4ee5\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u56e0\u6b64\u5176\u65b9\u5411\u5411\u91cf\u7684\u7b1b\u5361\u5c14\u5750\u6807\u5c31\u662f\u5206\u6bcd\u7684\u6570\u5b57\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-4ba6fe3a3d80f3a44c2c3a0c8345ffa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (6,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u4e24\u6761\u7ebf\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6211\u4eec\u786e\u5b9a\u4e24\u4e2a\u5411\u91cf\u7684\u6a21\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-565377b63a2e28ce9613745bc0c0b756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{(-4)^2+(-3)^2}= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"199\" 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-65100d7dbdf97aa72e9212379ff54de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{6^2+3^2}= \\sqrt{45}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5bf9\u89d2\u5ea6\u516c\u5f0f\u7684\u5411\u91cf\u4e4b\u95f4\u8fdb\u884c\u8fd0\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-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" 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-a36b58fc65b59f20656acc68016020ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(-4,-3) \\cdot (6,3)\\rvert}{5 \\cdot \\sqrt{45}}= \\cfrac{\\lvert -4 \\cdot 6 + (-3)\\cdot 3\\rvert}{33,54} = \\cfrac{33}{33,54} = 0,98\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"490\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u7528\u4f59\u5f26\u7684\u5012\u6570\u8ba1\u7b97\u4e24\u6761\u7ebf\u5f62\u6210\u7684\u89d2\u5ea6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-216ef184adb4e8e26ea4dba3a0d41a67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,98) = \\bm{10,30\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4e0b\u9762\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u662f\u591a\u5c11\uff1f <\/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-3a559370fd832ad2f4707782cf40cb37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=-2x+9 \\qquad s: \\ y=5x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"272\" 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\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u76f4\u7ebf\u659c\u7387\u7684\u65b9\u6cd5\u6765\u627e\u51fa\u5b83\u4eec\u6240\u6210\u7684\u89d2\u5ea6\uff0c\u56e0\u4e3a\u76f4\u7ebf\u662f\u663e\u5f0f\u65b9\u7a0b\u7684\u5f62\u5f0f\u3002<\/p>\n<p class=\"has-text-align-left\">\u6bcf\u6761\u7ebf\u7684\u659c\u7387\u662f\u4f34\u968f\u81ea\u53d8\u91cf\u7684\u6570\u5b57<\/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-845f2902b8bebf60c3c7372a7fbe4d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-42a36a89145f23919d8665908c3e2bc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/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-42de98336b7cbc2dc475ea3037bebc55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_s = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u659c\u7387\u516c\u5f0f\u6765\u786e\u5b9a\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-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" 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-172bd34124a3b9e86696158d992eebb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{-2-5}{1+5\\cdot (-2)} \\end{vmatrix}=\\begin{vmatrix} \\cfrac{-7}{-9} \\end{vmatrix} = 0,78\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"293\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u6211\u4eec\u901a\u8fc7\u53cd\u8f6c\u5207\u7ebf\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c84b4105875a851c576fb326e2ba6f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{tg}^{-1}(0,78) = \\bm{37,87\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u6c42\u901a\u8fc7\u8be5\u70b9\u7684\u76f4\u7ebf\u65b9\u7a0b<\/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-6958f848b3f39930bc315b56f627f888_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(5,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5e76\u4e0e\u7ebf\u6210 45\u00b0 \u89d2<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u88ab\u8bf4\u884c\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-34edcc0a8f3b1c557be083882ab8b7e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=2x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" 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\">\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u81f4\u7535<\/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>\u5230\u6211\u4eec\u8981\u8ba1\u7b97\u7684\u53f3\u8fb9\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u659c\u7387\u65b9\u6cd5\uff0c\u56e0\u4e3a\u6211\u4eec\u77e5\u9053\u76f4\u7ebf\u7684\u659c\u7387<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-9edd8ad155030a560ef8313513b5ac14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4ece\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f\uff08\u659c\u7387\u6cd5\uff09\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7ebf\u7684\u659c\u7387\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-580a84fe09f12aa20c352a8336880e41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5df2\u77e5\u503c\u4ee3\u5165\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-ace7fdfc7474a43a6fad81e0185d0050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(45\u00ba) =\\begin{vmatrix} \\cfrac{m_s-2}{1+2\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c1d\u8bd5\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\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-0f2ea68d68e24c3e30df526dfb88873c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =\\begin{vmatrix} \\cfrac{m_s-2}{1+2m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u65b9\u7a0b\u7684\u7edd\u5bf9\u503c\u4f7f\u5f97\u6c42\u89e3\u6709\u4e9b\u56f0\u96be\uff0c\u56e0\u4e3a\u4f60\u5fc5\u987b\u540c\u65f6\u5206\u6790\u6b63\u9009\u9879\u548c\u8d1f\u9009\u9879\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-149\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ad2ad90ee94f08746cea11db3a6917f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =+\\cfrac{m_s-2}{1+2m_s}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"110\" style=\"vertical-align: -15px;\"><\/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-56c4a065c3919fbe023153fe2ba9133c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 \\cdot (1+2m_s)=m_s-2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"173\" 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-d31fa5d4b608e062c0e15476b3f15e7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1+2m_s=m_s-2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"137\" style=\"vertical-align: -3px;\"><\/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-870381f6e915e33b32ad147c9a4de5fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2m_s-m_s=-2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"152\" style=\"vertical-align: -3px;\"><\/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-1d7c13f0d7d21af8c407f7f535e0d994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m_s=-3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b9e6f5eb952e8ea9758af5497ed8cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =-\\cfrac{m_s-2}{1+2m_s}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"110\" style=\"vertical-align: -15px;\"><\/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-2b984c3bc74269597752a909f457c8ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 \\cdot (1+2m_s)=-(m_s-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" 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-df53d7b057ec0e6b6f7701fb5149cbe0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1+2m_s=-m_s+2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"151\" style=\"vertical-align: -3px;\"><\/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-9a96107cb59f52dcf9bb703e54c27757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2m_s+m_s=2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"138\" style=\"vertical-align: -3px;\"><\/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-067dac6d6aea31f65caccf5ed9c30052_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 3m_s=1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: -3px;\"><\/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-9003dbf8679e5b0aaa8c10777f6d38fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m_s=\\cfrac{1}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"57\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6848\uff1a\u4e00\u6761\u659c\u7387\u4e3a -3 \u7684\u7ebf\u548c\u53e6\u4e00\u6761\u659c\u7387\u4e3a\u4e09\u5206\u4e4b\u4e00\u7684\u7ebf\u3002<\/p>\n<p class=\"has-text-align-left\">\u76f4\u7ebf\u7684\u70b9\u659c\u7387\u65b9\u7a0b\u7684\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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u4e24\u6761\u53ef\u80fd\u7684\u76f4\u7ebf\u7684\u659c\u7387\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6839\u636e\u4ee5\u4e0b\u8bed\u53e5\u5199\u51fa\u6bcf\u6761\u76f4\u7ebf\u7684\u70b9\u659c\u7387\u65b9\u7a0b\u4ee5\u53ca\u5b83\u4eec\u5fc5\u987b\u7ecf\u8fc7\u7684\u70b9\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8726fb72614f7e8f7e546f9ac6995cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(5,-1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" 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-0a69157a1cf6a00b750b804590e63524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ y+1=-3(x-5) \\qquad \\qquad s': \\ y+1=\\cfrac{1}{3}(x-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"402\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5982\u4f55\u8ba1\u7b97\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff08\u516c\u5f0f\uff09\u7684\u8bf4\u660e\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%b8%a4%e6%9d%a1%e7%ba%bf%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%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0%e6%96%9c%e7%8e%87%e5%af%bc%e6%bc%94%e5%90%91\/\"> <span class=\"screen-reader-text\">\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\uff08\u516c\u5f0f\uff09<\/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-227","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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