{"id":3483,"date":"2025-05-06T23:56:49","date_gmt":"2025-05-06T15:56:49","guid":{"rendered":"https:\/\/www.haruhi.fans\/?p=3483"},"modified":"2025-06-08T21:52:41","modified_gmt":"2025-06-08T13:52:41","slug":"%e8%ae%a1%e7%ae%97%e6%9c%ba%e5%9b%be%e5%bd%a2%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/www.haruhi.fans\/?p=3483","title":{"rendered":"\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66"},"content":{"rendered":"\n

\u77e9\u9635\u4e0e\u5411\u91cf<\/h2>\n\n\n\n

\u70b9\u4e58\u4e0e\u53c9\u4e58<\/h3>\n\n\n\n

\u70b9\u4e58 dot(A,B)<\/strong><\/h4>\n\n\n\n
    \n
  1. \u4e24\u5355\u4f4d\u5411\u91cf\u7684\u70b9\u4e58 = \u4e24\u5355\u4f4d\u5411\u91cf\u5939\u89d2\u7684cos\u503c a \u00b7 b = abcos\u03b8 = cos\u03b8<\/li>\n\n\n\n
  2. \u5206\u91cf\u76f8\u4e58\u540e\u76f8\u52a0\uff1ba=vec(x1,y1)\uff0cb=vec(x2,y2)\uff0c\u5219a dot b = x1x2 + y1y2\uff0ca dot b =|a||b|cos\u03b8<\/li>\n\n\n\n
  3. a dot b \u4e3ab\u5728a\u4e0a\u7684\u6295\u5f71\u957f\u5ea6\u4e0eb\u6a21\u957f\u7684\u4e58\u79ef<\/li>\n<\/ol>\n\n\n\n

    $$
    \\vec{a} \\cdot \\vec{b} =
    \\begin{pmatrix}
    x_a & y_a & z_a
    \\end{pmatrix}
    \\begin{pmatrix}
    x_b \\\\
    y_b \\\\
    z_b
    \\end{pmatrix}
    $$<\/p>\n\n\n\n

    \u610f\u4e49\uff1a<\/strong><\/p>\n\n\n\n

      \n
    1. \u4e24\u5355\u4f4d\u5411\u91cf\u70b9\u4e58\u7684\u503c\u8303\u56f4\u5728[-1,1]\uff0c\u63cf\u8ff0\u4e24\u5355\u4f4d\u5411\u91cf\u7684\u201c\u63a5\u8fd1\u7a0b\u5ea6\u201d\uff0c\u5782\u76f4or\u540c\u5411or\u53cd\u5411<\/li>\n\n\n\n
    2. \u627e\u6295\u5f71\uff1a\u67d0\u4e16\u754c\u5750\u6807\u4e0e\u67d0\u5355\u4f4d\u5411\u91cf\u70b9\u4e58\uff0c\u7ed3\u679c\u4e3a\u8be5\u4e16\u754c\u5750\u6807\u5728\u8be5\u5411\u91cf\u4e0a\u7684\u6295\u5f71\u70b9\u7684\u5750\u6807<\/li>\n<\/ol>\n\n\n\n

      \u53c9\u4e58 A cross B<\/strong><\/h4>\n\n\n\n

      A X B = ABsin\u03c6\uff0c\u53f3\u624b\u5148\u7a7f\u8fc7A\u518d\u7a7f\u8fc7B\uff0c\u5927\u62c7\u6307\u65b9\u5411\u4e3a\u53c9\u4e58\u65b9\u5411<\/p>\n\n\n\n

      $$ \\vec{a} \\times \\vec{b} = \\begin{pmatrix} y_a z_b – y_b z_a \\\\ z_a x_b – x_a z_b \\\\ x_a y_b – y_a x_b \\end{pmatrix} $$<\/p>\n\n\n\n

      $$
      \\vec{a} \\times \\vec{b} = A^* \\vec{b} =
      \\begin{pmatrix}
      0 & -z_a & y_a \\\\
      z_a & 0 & -x_a \\\\
      -y_a & x_a & 0
      \\end{pmatrix}
      \\begin{pmatrix}
      x_b \\\\
      y_b \\\\
      z_b
      \\end{pmatrix}
      $$<\/p>\n\n\n\n

      \u610f\u4e49\uff1a
      1.\u540c\u4e00\u4e2a\u5e73\u9762\u5185\u786e\u5b9a\u65b9\u5411\uff08\u6b63\u8d1f\uff09\uff0c\u662f\u5de6\u8fd8\u662f\u53f3\uff08\u6bd4\u5982b\u5728a\u7684\u9006\u65f6\u9488\u65b9\u5411\uff09
      2.\u5224\u65ad\u4e00\u4e2a\u70b9\u662f\u5426\u5728\u56fe\u5f62\u5185\u90e8 \u3002\u5982\u4e0b\u56fe\uff0c\u901a\u8fc7CA\uff0cCP\u53ef\u4ee5\u5224\u65adP\u5728AC\u9006\u65f6\u9488\u65b9\u5411\uff0c\u540c\u7406\u5224\u65ad\u4e09\u4e2a\uff0c\u90fd\u662f\u4e00\u4e2a\u65b9\u5411\u7684\u8bdd\u5c31\u5728\u5185\u90e8\uff0c\u53ef\u4ee5\u5f97\u5230P\u7684\u4f4d\u7f6e\u5173\u7cfb<\/p>\n\n\n\n

      \"\"<\/div><\/figure>\n\n\n\n

      \u77e9\u9635<\/h3>\n\n\n\n

      \u77e9\u9635\u4e58\u6cd5<\/h4>\n\n\n\n

      \u4ec0\u4e48\u65f6\u5019\u53ef\u4ee5\u4e58\uff1f (M x N)(N<\/strong> x P) = (M x P)\uff0c\u4e2d\u95f4\u76f8\u540c\u5373\u53ef\u3002\u8ba1\u7b97\u5c31\u662f\u627e\u5bf9\u5e94\u7684\u5411\u91cf\u70b9\u4e58\u51fa\u7ed3\u679c<\/p>\n\n\n\n