{"id":1507,"date":"2024-11-08T15:23:50","date_gmt":"2024-11-08T07:23:50","guid":{"rendered":"https:\/\/thereisno.top\/?p=1507"},"modified":"2024-11-09T22:24:10","modified_gmt":"2024-11-09T14:24:10","slug":"%e7%9b%b4%e7%ba%bf%e4%b8%8e%e5%b9%b3%e9%9d%a2%e7%9a%84%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/thereisno.top\/?p=1507","title":{"rendered":"\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a"},"content":{"rendered":"\n

\u5728\u521d\u4e2d\u6211\u4eec\u5c31\u5b66\u8fc7\u5f88\u591a\u79cd\u76f4\u7ebf\u7684\u8868\u793a<\/p>\n

\n

\u4e00\u822c\u5f0f<\/strong>\uff1a A<\/mi>x<\/mi>+<\/mo>B<\/mi>y<\/mi>+<\/mo>C<\/mi>=<\/mo>0<\/mn><\/mrow>Ax+By+C=0<\/annotation><\/semantics><\/math> A<\/mi>,<\/mo>B<\/mi><\/mrow>A,B<\/annotation><\/semantics><\/math>\u4e0d\u80fd\u540c\u65f6\u4e3a\u96f6\uff1b
\n\u659c\u622a\u5f0f<\/strong>\uff1a y<\/mi>=<\/mo>k<\/mi>x<\/mi>+<\/mo>b<\/mi><\/mrow>y = kx + b<\/annotation><\/semantics><\/math> ,\u5176\u4e2d k<\/mi>k<\/annotation><\/semantics><\/math> \u662f\u659c\u7387(slope)\uff0c\u8868\u793a\u76f4\u7ebf\u4e0ex\u8f74\u6b63\u65b9\u5411\u5939\u89d2\u7684\u6b63\u5207\u503c\uff0cb<\/mi>b<\/annotation><\/semantics><\/math> \u662f\u7eb5\u622a\u8ddd(y-intercept,\u622a\u8ddd\u53ef\u4ee5\u662f\u8d1f\u503c<\/strong>)\uff0c\u8868\u793a\u76f4\u7ebf\u4e0ey\u8f74\u7684\u4ea4\u70b9\u7684\u7eb5\u5750\u6807\uff1b
\n\u70b9\u659c\u7387<\/strong>\uff1a y<\/mi>\u2212<\/mo>y<\/mi>1<\/mn><\/msub>=<\/mo>k<\/mi>(<\/mo>x<\/mi>\u2212<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow><\/mrow>y – y_{1} = k(x – x_{1})<\/annotation><\/semantics><\/math>,\u5176\u4e2d (<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>(x_{1},y_{1})<\/annotation><\/semantics><\/math> \u8868\u793a\u76f4\u7ebf\u4e0a\u4e00\u70b9\uff0c k<\/mi>k<\/annotation><\/semantics><\/math>\u8868\u793a\u76f4\u7ebf\u659c\u7387\uff1b
\n\u622a\u8ddd\u5f0f<\/strong>\uff1a x<\/mi>a<\/mi><\/mfrac>+<\/mo>y<\/mi>b<\/mi><\/mfrac>=<\/mo>1<\/mn><\/mrow>\\frac{x}{a} + \\frac{y}{b} = 1<\/annotation><\/semantics><\/math>,\u5176\u4e2d a<\/mi>,<\/mo>b<\/mi><\/mrow>a,b<\/annotation><\/semantics><\/math>\u5206\u522b\u8868\u793a\u76f4\u7ebf\u4e0ex\u8f74\u548cy\u8f74\u7684\u622a\u8ddd\uff0c\u4e5f\u5c31\u662f\u4e0ex\u8f74\u4ea4\u70b9\u7684\u6a2a\u5750\u6807\u548c\u4e0ey\u8f74\u4ea4\u70b9\u7684\u7eb5\u5750\u6807\uff1b
\n\u4e24\u70b9\u5f0f<\/strong>\uff1a x<\/mi>\u2212<\/mo>x<\/mi>1<\/mn><\/msub><\/mrow>x<\/mi>2<\/mn><\/msub>\u2212<\/mo>x<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac>=<\/mo>y<\/mi>\u2212<\/mo>y<\/mi>1<\/mn><\/msub><\/mrow>y<\/mi>2<\/mn><\/msub>\u2212<\/mo>y<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac><\/mrow>\\frac{x – x_{1}}{x_{2} – x_{1}} = \\frac{y – y_{1}}{y_{2} – y_{1}}<\/annotation><\/semantics><\/math>\uff0c\u5176\u4e2d (<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>,<\/mo>(<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>y<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow><\/mrow>(x_{1},y_{1}),(x_{2},y_{2})<\/annotation><\/semantics><\/math> \u8868\u793a\u76f4\u7ebf\u4e0a\u4e24\u70b9\u5750\u6807\uff1b<\/p>\n<\/blockquote>\n\n\n\n\n\n\n\n

\u4e0a\u8ff0\u8fd9\u4e9b\uff0c\u6211\u4eec\u5b66\u7684\u90fd\u662f\u5728\u4e8c\u7ef4\u5e73\u9762\u4e2d\u7684\u76f4\u7ebf\u8868\u793a\uff0c\u5982\u679c\u5230\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u76f4\u7ebf\u8be5\u5982\u4f55\u8868\u793a\u5462\uff1f\u90a3\u4e48\u8fdb\u4e00\u6b65\u4e00\u4e2a\u5e73\u9762\u53c8\u8be5\u5982\u4f55\u8868\u793a\u5462\uff1f<\/p>\n

\u90a3\u4e48\u672c\u6587\u5c31\u6765\u4ecb\u7ecd\u4e00\u4e0b\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a\u3002<\/strong><\/p>\n

\n

\u4e00\u3001\u76f4\u7ebf\u7684\u5411\u91cf\u8868\u793a<\/strong><\/h2>\n

\u5df2\u77e5\u76f4\u7ebf\u4e0a\u70b9 A<\/mi>A<\/annotation><\/semantics><\/math>\u548c\u76f4\u7ebf\u7684\u7684\u65b9\u5411\u5411\u91cf b<\/mi>\u2192<\/mo><\/mover>\\overset{\\rightarrow}{b}<\/annotation><\/semantics><\/math> ,\u6839\u636e\u5411\u91cf\u7684\u52a0\u6cd5\u8fd0\u7b97\u5c31\u53ef\u4ee5\u628a\u76f4\u7ebf\u4e0a\u4efb\u610f\u4e00\u70b9 R<\/mi>R<\/annotation><\/semantics><\/math>\u90fd\u53ef\u4ee5\u8868\u793a\u51fa\u6765\u3002<\/p>\n

<\/p>\n

\u56e0\u4e3aO<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>O<\/mi>A<\/mi><\/mrow>\u2192<\/mo><\/mover>+<\/mo>A<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover><\/mrow>\\overset{\\rightarrow}{OR} = \\overset{\\rightarrow}{OA} + \\overset{\\rightarrow}{AR}<\/annotation><\/semantics><\/math> , A<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>\u03bb<\/mi>b<\/mi>\u2192<\/mo><\/mover><\/mrow>\\overset{\\rightarrow}{AR} = \\lambda\\overset{\\rightarrow}{b}<\/annotation><\/semantics><\/math> \uff0c<\/p>\n

\u6240\u4ee5\uff0cO<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>O<\/mi>A<\/mi><\/mrow>\u2192<\/mo><\/mover>+<\/mo>\u03bb<\/mi>b<\/mi>\u2192<\/mo><\/mover><\/mrow>\\overset{\\rightarrow}{OR} = \\overset{\\rightarrow}{OA} + \\lambda\\overset{\\rightarrow}{b}<\/annotation><\/semantics><\/math><\/p>\n

\u8fd9\u53ef\u4ee5\u7406\u89e3\u4e3a\u76f4\u7ebf\u4e0a\u4efb\u610f\u4e00\u70b9\u90fd\u53ef\u4ee5\u7531\u76f4\u7ebf\u4e0a\u4e00\u5df2\u77e5\u70b9\u6309\u7167\u65b9\u5411\u5411\u91cf\u5e73\u79fb\u5f97\u5230<\/strong>\u3002\u6839\u636e\u4e0a\u8ff0\u539f\u7406\u6211\u4eec\u53ef\u4ee5\u5230\u76f4\u7ebf\u5728\u4e8c\u7ef4\u3001\u4e09\u7ef4\u60c5\u51b5\u4e0b\u7684\u5411\u91cf\u8868\u793a\u3002<\/p>\n

\uff081\uff09\u4e8c\u7ef4<\/strong>\u76f4\u7ebf\u5411\u91cf\u8868\u793a<\/p>\n

(<\/mo>x<\/mi><\/mtd><\/mtr>y<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>x<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>0<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bb<\/mi>(<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\left( \\begin{array}{l} x \\\\ y \\\\ \\end{array} \\right) = \\left( \\begin{array}{l} x_{0} \\\\ y_{0} \\\\ \\end{array} \\right) + \\lambda\\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math><\/p>\n

\u5176\u4e2d (<\/mo>x<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>0<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} x_{0} \\\\ y_{0} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math>\u662f\u76f4\u7ebf\u4e0a\u70b9\u5750\u6807\uff0c (<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math>\u662f\u65b9\u5411\u5411\u91cf\uff0c \u03bb<\/mi>\\lambda<\/annotation><\/semantics><\/math>\u662f\u53c2\u6570\u3002<\/p>\n

\u6839\u636e\u4e0a\u8ff0\u5f0f\u5b50\u5f88\u5bb9\u6613\u5f97\u5230\u76f4\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b\uff1a<\/p>\n

{<\/mo>x<\/mi>=<\/mo>x<\/mi>0<\/mn><\/msub>+<\/mo>\u03bb<\/mi>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>=<\/mo>y<\/mi>0<\/mn><\/msub>+<\/mo>\u03bb<\/mi>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/mrow>\\left\\{ \\begin{array}{l} {x = x_{0} + \\lambda b_{1}} \\\\ {y = y_{0} + \\lambda b_{2}} \\\\ \\end{array} \\right.<\/annotation><\/semantics><\/math> \uff0c<\/p>\n

\u4e5f\u628a \u03bb<\/mi>\\lambda<\/annotation><\/semantics><\/math> \u6d88\u53bb\u5f97\u5230\u76f4\u7ebf\u7684\u7b1b\u5361\u5c14\u5750\u6807\u5f62\u5f0f\uff1a<\/p>\n

x<\/mi>\u2212<\/mo>x<\/mi>0<\/mn><\/msub><\/mrow>b<\/mi>1<\/mn><\/msub><\/mfrac>=<\/mo>y<\/mi>\u2212<\/mo>y<\/mi>0<\/mn><\/msub><\/mrow>b<\/mi>2<\/mn><\/msub><\/mfrac><\/mrow>\n\\frac{x – x_{0}}{b_{1}} = \\frac{y – y_{0}}{b_{2}}\n<\/annotation><\/semantics><\/math><\/p>\n

\uff082\uff09\u4e09\u7ef4<\/strong>\u76f4\u7ebf\u5411\u91cf\u8868\u793a<\/p>\n

(<\/mo>x<\/mi><\/mtd><\/mtr>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>x<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>z<\/mi>0<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bb<\/mi>(<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\left( \\begin{array}{l} x \\\\ y \\\\ z \\\\ \\end{array} \\right) = \\left( \\begin{array}{l} x_{0} \\\\ y_{0} \\\\ z_{0} \\\\ \\end{array} \\right) + \\lambda\\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ b_{3} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math><\/p>\n

\u5176\u4e2d (<\/mo>x<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>z<\/mi>0<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} x_{0} \\\\ y_{0} \\\\ z_{0} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math>\u662f\u76f4\u7ebf\u4e0a\u4e00\u70b9\uff0c (<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ b_{3} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math>\u662f\u65b9\u5411\u5411\u91cf\u3002<\/p>\n

\u540c\u7406\u53ef\u4ee5\u5230\u76f4\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b\uff1a<\/p>\n

{<\/mo>x<\/mi>=<\/mo>x<\/mi>0<\/mn><\/msub>+<\/mo>\u03bb<\/mi>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>=<\/mo>y<\/mi>0<\/mn><\/msub>+<\/mo>\u03bb<\/mi>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>z<\/mi>=<\/mo>z<\/mi>0<\/mn><\/msub>+<\/mo>\u03bb<\/mi>b<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/mrow>\\left\\{ \\begin{array}{l} {x = x_{0} + \\lambda b_{1}} \\\\ {y = y_{0} + \\lambda b_{2}} \\\\ {z = z_{0} + \\lambda b_{3}} \\\\ \\end{array}\\right.<\/annotation><\/semantics><\/math><\/p>\n

\u7b1b\u5361\u5c14\u5750\u6807\u5f62\u5f0f:<\/p>\n

x<\/mi>\u2212<\/mo>x<\/mi>0<\/mn><\/msub><\/mrow>b<\/mi>1<\/mn><\/msub><\/mfrac>=<\/mo>y<\/mi>\u2212<\/mo>y<\/mi>0<\/mn><\/msub><\/mrow>b<\/mi>2<\/mn><\/msub><\/mfrac>=<\/mo>z<\/mi>\u2212<\/mo>z<\/mi>0<\/mn><\/msub><\/mrow>b<\/mi>3<\/mn><\/msub><\/mfrac><\/mrow>\n\\frac{x – x_{0}}{b_{1}} = \\frac{y – y_{0}}{b_{2}} = \\frac{z – z_{0}}{b_{3}}\n<\/annotation><\/semantics><\/math><\/p>\n

\u6bd4\u5982\u7ed9\u4e00\u76f4\u7ebf\u65b9\u7a0b x<\/mi>\u2212<\/mo>1<\/mn><\/mrow>2<\/mn><\/mfrac>=<\/mo>3<\/mn>+<\/mo>y<\/mi><\/mrow>3<\/mn><\/mfrac>=<\/mo>z<\/mi><\/mrow>\\frac{x – 1}{2} = \\frac{3 + y}{3} = z<\/annotation><\/semantics><\/math>\uff0c<\/p>\n

\u90a3\u4e48\u53ef\u4ee5\u77e5\u9053\u8be5\u76f4\u7ebf\u8fc7 (<\/mo>1<\/mn>,<\/mo>\u2212<\/mo>3<\/mn>,<\/mo>0<\/mn>)<\/mo><\/mrow>(1,-3,0)<\/annotation><\/semantics><\/math> \uff0c\u4e14\u65b9\u5411\u5411\u91cf\u4e3a (<\/mo>2<\/mn><\/mtd><\/mtr>3<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} 2 \\\\ 3 \\\\ 1 \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \u3002<\/p>\n
\n

\u4e8c\u3001\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a<\/strong><\/h2>\n

\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5:\u4e00\u79cd\u662f\u5229\u7528\u5411\u91cf\u7684\u5408\u6210\uff0c\u4e00\u79cd\u662f\u5229\u7528\u6cd5\u5411\u91cf\u3002<\/p>\n

\uff081\uff09\u5411\u91cf\u7684\u5408\u6210<\/strong><\/p>\n

<\/p>\n

\u5982\u679c\u5df2\u77e5\u5e73\u9762\u5185\u4e00\u70b9 A<\/mi>(<\/mo>a<\/mi>1<\/mn><\/msub>,<\/mo>a<\/mi>2<\/mn><\/msub>,<\/mo>a<\/mi>3<\/mn><\/msub>)<\/mo><\/mrow><\/mrow>A\\left( a_{1},a_{2},a_{3} \\right)<\/annotation><\/semantics><\/math><\/p>\n

\u548c\u4e24\u4e2a\u4e0d\u5e73\u884c\u7684\u5411\u91cf<\/strong> b<\/mi>\u2192<\/mo><\/mover>=<\/mo>(<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\overset{\\rightarrow}{b} = \\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ b_{3} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \u548c c<\/mi>\u2192<\/mo><\/mover>=<\/mo>(<\/mo>c<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>c<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>c<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\overset{\\rightarrow}{c} = \\left( \\begin{array}{l} c_{1} \\\\ c_{2} \\\\ c_{3} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \uff0c\u90a3\u4e48\u5e73\u9762\u5185\u4efb\u610f\u4e00\u70b9 R<\/mi>R<\/annotation><\/semantics><\/math> \u90fd\u5b58\u5728\u5e38\u6570\u03bb<\/mi>,<\/mo>\u03bc<\/mi><\/mrow>\\lambda,\\mu<\/annotation><\/semantics><\/math>\u4f7f\u5f97\u4e0b\u5f0f\u6210\u7acb\uff1a<\/p>\n

A<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>\u03bb<\/mi>b<\/mi>\u2192<\/mo><\/mover>+<\/mo>\u03bc<\/mi>c<\/mi>\u2192<\/mo><\/mover><\/mrow>\\overset{\\rightarrow}{AR} = \\lambda\\overset{\\rightarrow}{b} + \\mu\\overset{\\rightarrow}{c}<\/annotation><\/semantics><\/math> ,<\/p>\n

\u53c8\u56e0\u4e3a O<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>O<\/mi>A<\/mi><\/mrow>\u2192<\/mo><\/mover>+<\/mo>\u03bb<\/mi>b<\/mi>\u2192<\/mo><\/mover>+<\/mo>\u03bc<\/mi>c<\/mi>\u2192<\/mo><\/mover><\/mrow>\\overset{\\rightarrow}{OR} = \\overset{\\rightarrow}{OA} + \\lambda\\overset{\\rightarrow}{b} + \\mu\\overset{\\rightarrow}{c}<\/annotation><\/semantics><\/math> ,\u5373\uff1a<\/p>\n

(<\/mo>x<\/mi><\/mtd><\/mtr>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>a<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>a<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>a<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bb<\/mi>(<\/mo>b<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>b<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bc<\/mi>(<\/mo>c<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>c<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>c<\/mi>3<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\left( \\begin{array}{l} x \\\\ y \\\\ z \\\\ \\end{array} \\right) = \\left( \\begin{array}{l} a_{1} \\\\ a_{2} \\\\ a_{3} \\\\ \\end{array} \\right) + \\lambda\\left( \\begin{array}{l} b_{1} \\\\ b_{2} \\\\ b_{3} \\\\ \\end{array} \\right) + \\mu\\left( \\begin{array}{l} c_{1} \\\\ c_{2} \\\\ c_{3} \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math><\/p>\n

\u6211\u4eec\u4e8c\u7ef4\u7684\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e5f\u53ef\u4ee5\u770b\u6210\u662f\u4e24\u4e2a\u76f8\u4e92\u5782\u76f4\u7684\u57fa\u5411\u91cf\u52a0\u51cf\u8fd0\u7b97\u5f97\u5230\uff1a<\/p>\n

(<\/mo>x<\/mi><\/mtd><\/mtr>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>0<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bb<\/mi>(<\/mo>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>+<\/mo>\u03bc<\/mi>(<\/mo>0<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\left( \\begin{array}{l} x \\\\ y \\\\ z \\\\ \\end{array} \\right) = \\left( \\begin{array}{l} 0 \\\\ 0 \\\\ 0 \\\\ \\end{array} \\right) + \\lambda\\left( \\begin{array}{l} 1 \\\\ 0 \\\\ 0 \\\\ \\end{array} \\right) + \\mu\\left( \\begin{array}{l} 0 \\\\ 1 \\\\ 0 \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math><\/p>\n

\uff082\uff09\u6cd5\u5411\u91cf<\/strong><\/p>\n

<\/p>\n

\u628a\u4e0e\u5e73\u9762\u4e2d\u4efb\u610f\u5411\u91cf\u90fd\u76f8\u4e92\u5782\u76f4\u7684\u5411\u91cf\u79f0\u4e3a\u6cd5\u5411\u91cf\u3002\u5982\u679c\u5df2\u77e5\u5e73\u9762\u4e0a\u4e00\u70b9 A<\/mi>(<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>1<\/mn><\/msub>,<\/mo>z<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow><\/mrow>A\\left( x_{1},y_{1},z_{1} \\right)<\/annotation><\/semantics><\/math> \u548c\u5e73\u9762\u7684\u6cd5\u5411\u91cf n<\/mi>\u2192<\/mo><\/mover>=<\/mo>(<\/mo>a<\/mi><\/mtd><\/mtr>b<\/mi><\/mtd><\/mtr>c<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\\overset{\\rightarrow}{n} = \\left( \\begin{array}{l} a \\\\ b \\\\ c \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \uff0c\u90a3\u4e48\u70b9 A<\/mi>A<\/annotation><\/semantics><\/math> \u548c\u5e73\u9762\u5185\u4efb\u610f\u4e00\u70b9 R<\/mi>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo><\/mrow><\/mrow>R(x,y,z)<\/annotation><\/semantics><\/math> \u6240\u6784\u6210\u7684\u5411\u91cf A<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>\\overset{\\rightarrow}{AR}<\/annotation><\/semantics><\/math> \u4e0e\u6cd5\u5411\u91cf\u5782\u76f4\u53ef\u5f97\uff1a<\/p>\n

n<\/mi>\u2192<\/mo><\/mover>\u2022<\/mo>A<\/mi>R<\/mi><\/mrow>\u2192<\/mo><\/mover>=<\/mo>0<\/mn><\/mrow>\\overset{\\rightarrow}{n} \\bullet \\overset{\\rightarrow}{AR} = 0<\/annotation><\/semantics><\/math><\/p>\n

(<\/mo>a<\/mi><\/mtd><\/mtr>b<\/mi><\/mtd><\/mtr>c<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\u22c5<\/mo>(<\/mo>x<\/mi>\u2212<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>\u2212<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>z<\/mi>\u2212<\/mo>z<\/mi>1<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>0<\/mn><\/mrow>\\left( \\begin{array}{l} a \\\\ b \\\\ c \\\\ \\end{array} \\right) \\cdot \\left( \\begin{array}{l} {x – x_{1}} \\\\ {y – y_{1}} \\\\ {z – z_{1}} \\\\ \\end{array} \\right) = 0<\/annotation><\/semantics><\/math><\/p>\n

\u6240\u4ee5\uff0ca<\/mi>(<\/mo>x<\/mi>\u2212<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>+<\/mo>b<\/mi>(<\/mo>y<\/mi>\u2212<\/mo>y<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>+<\/mo>c<\/mi>(<\/mo>z<\/mi>\u2212<\/mo>z<\/mi>1<\/mn><\/msub>)<\/mo><\/mrow>=<\/mo>0<\/mn><\/mrow>a\\left( x – x_{1} \\right) + b\\left( y – y_{1} \\right) + c\\left( z – z_{1} \\right) = 0<\/annotation><\/semantics><\/math><\/p>\n

\u5f97\u5230\u5e73\u9762\u7684\u4e00\u822c\u65b9\u7a0b\uff1a<\/p>\n

a<\/mi>x<\/mi>+<\/mo>b<\/mi>y<\/mi>+<\/mo>c<\/mi>z<\/mi>=<\/mo>a<\/mi>x<\/mi>1<\/mn><\/msub>+<\/mo>b<\/mi>y<\/mi>1<\/mn><\/msub>+<\/mo>c<\/mi>z<\/mi>1<\/mn><\/msub><\/mrow>ax + by + cz = ax_{1} + by_{1} + cz_{1}<\/annotation><\/semantics><\/math> .<\/p>\n

\u56e0\u6b64\uff0c\u578b\u5982A<\/mi>x<\/mi>+<\/mo>B<\/mi>y<\/mi>+<\/mo>C<\/mi>z<\/mi>=<\/mo>D<\/mi><\/mrow>Ax + By + Cz = D<\/annotation><\/semantics><\/math> \u7684\u90fd\u662f\u5e73\u9762\u65b9\u7a0b\uff0c\u4e14 (<\/mo>A<\/mi><\/mtd><\/mtr>B<\/mi><\/mtd><\/mtr>C<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} A \\\\ B \\\\ C \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \u662f\u8be5\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u3002<\/p>\n

\u6bd4\u5982\u7ed9\u4e00\u5e73\u9762\u65b9\u7a0b 2<\/mn>x<\/mi>+<\/mo>4<\/mn>y<\/mi>+<\/mo>z<\/mi>=<\/mo>1<\/mn><\/mrow>2x + 4y + z = 1<\/annotation><\/semantics><\/math>\uff0c\u90a3\u4e48\u8be5\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u4e3a (<\/mo>2<\/mn><\/mtd><\/mtr>4<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} 2 \\\\ 4 \\\\ 1 \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \uff1b\u90a3\u4e48\u5982\u679c\u5e73\u9762\u65b9\u7a0b\u4e3a 3<\/mn>x<\/mi>+<\/mo>5<\/mn>y<\/mi>=<\/mo>1<\/mn><\/mrow>3x + 5y = 1<\/annotation><\/semantics><\/math> \u5176\u6cd5\u5411\u91cf\u4e3a\u591a\u5c11\u5462\uff1f<\/p>\n

\u5176\u6cd5\u5411\u91cf\u4e3a(<\/mo>3<\/mn><\/mtd><\/mtr>5<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>\\left( \\begin{array}{l} 3 \\\\ 5 \\\\ 0 \\\\ \\end{array} \\right)<\/annotation><\/semantics><\/math> \u3002<\/p>\n

\u81f3\u6b64\uff0c\u76f4\u7ebf\u548c\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a\u90fd\u5df2\u7ecf\u4ecb\u7ecd\u5b8c\u6bd5\uff0c\u5728\u6b64\u57fa\u7840\u4e0a\u5411\u91cf\u8fd8\u6709\u4e24\u4e2a\u91cd\u8981\u7684\u5e94\u7528\uff1a\u8ddd\u79bb\u4e0e\u5939\u89d2\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5728\u521d\u4e2d\u6211\u4eec\u5c31\u5b66\u8fc7\u5f88\u591a\u79cd\u76f4\u7ebf\u7684\u8868\u793a \u4e00\u822c\u5f0f\uff1a Ax+By+C=0Ax+By+C=0 A,BA,B\u4e0d\u80fd\u540c\u65f6\u4e3a\u96f6\uff1b … <\/p>\n

\u7ee7\u7eed\u9605\u8bfb\u201c\u76f4\u7ebf\u4e0e\u5e73\u9762\u7684\u5411\u91cf\u8868\u793a\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[89],"tags":[90],"class_list":["post-1507","post","type-post","status-publish","format-standard","hentry","category-89","tag-90"],"_links":{"self":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1507","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1507"}],"version-history":[{"count":5,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1507\/revisions"}],"predecessor-version":[{"id":1525,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1507\/revisions\/1525"}],"wp:attachment":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}