{"id":4953,"date":"2014-03-05T06:00:27","date_gmt":"2014-03-04T21:00:27","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4953"},"modified":"2014-09-10T16:42:38","modified_gmt":"2014-09-10T07:42:38","slug":"post-4953","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4953","title":{"rendered":"\u30c9\u30c3\u30c8\u7a4d\u307e\u305f\u306f\u30b9\u30ab\u30e9\u30fc\u7a4d"},"content":{"rendered":"

\u30002\u3064\u306e\u30d9\u30af\u30c8\u30eb \\bold{A} \u3068 \\bold{B} \u306e\u30c9\u30c3\u30c8\u7a4d\u307e\u305f\u306f\u30b9\u30ab\u30e9\u30fc\u7a4d\u306f \\bold{A}\\cdot\\bold{B} \u3068\u8a18\u8ff0\u3057\uff08\\bold{A} \u30c9\u30c3\u30c8 \\bold{B} \u3068\u8aad\u3080\uff09 \\bold{A} \u304a\u3088\u3073 \\bold{B} \u306e\u5927\u304d\u3055\u306e\u7a4d\u3068\uff0c\u4e21\u8005\u306e\u306a\u3059\u89d2\u306e\u30b3\u30b5\u30a4\u30f3\u3068\u306e\u7a4d\u3068\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u8a18\u53f7\u3067\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8a18\u3057\u307e\u3059\uff0e<\/p>\n

\\bold{A}\\cdot\\bold{B} = AB\\cos\\theta,\\ 0\\le\\theta\\le\\pi\\cdots(4)<\/p>\n

\u3000\u7279\u306b \\bold{A}\\cdot\\bold{B} \u306f\u30b9\u30ab\u30e9\u30fc\u3067\u3042\u3063\u3066\u30d9\u30af\u30c8\u30eb\u3067\u306f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff0e<\/p>\n

\u3000\u4e0b\u8a18\u306e\u6cd5\u5247\u304c\u6709\u52b9\u3067\u3059\uff0e<\/p>\n

    \n
  1. \\bold{A}\\cdot\\bold{B} = \\bold{B}\\cdot\\bold{A}<\/li>\n

    \u30c9\u30c3\u30c8\u7a4d\u306e\u4ea4\u63db\u6cd5\u5247<\/p>\n

  2. \\bold{A}\\cdot(\\bold{B} + \\bold{C}) = \\bold{A}\\cdot\\bold{B} + \\bold{A}\\cdot\\bold{C}<\/li>\n

    \u5206\u914d\u6cd5\u5247<\/p>\n

  3. m(\\bold{A}\\cdot\\bold{B}) = (m\\bold{A})\\cdot\\bold{B} = \\bold{A}\\cdot(m\\bold{\\bold{B}}) = (\\bold{A}\\cdot\\bold{B})m<\/li>\n

    \u3053\u3053\u3067 m \u306f\u30b9\u30ab\u30e9\u30fc\u3067\u3059\uff0e<\/p>\n

  4. \\bold{i}\\cdot\\bold{i} = \\bold{j}\\cdot\\bold{j} = \\bold{k}\\cdot\\bold{k} = 1,\\ \\bold{i}\\cdot\\bold{j} = \\bold{j}\\cdot\\bold{k} = \\bold{k}\\cdot\\bold{i} = 0<\/li>\n
  5. \u4eee\u306b \\bold{A} = A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k} \u304b\u3064 \\bold{B} = B_1\\bold{i} + B_2\\bold{j} + B_3\\bold{k} \u3067\u3042\u308b\u306a\u3089<\/li>\n
      \n
    • \\bold{A}\\cdot\\bold{B} = A_1B_1 + A_2B_2 + A_3B_3<\/li>\n
    • \\bold{A}\\cdot\\bold{A} = A^2 = A_1^2 + A_2^2 + A_3^2<\/li>\n
    • \\bold{B}\\cdot\\bold{B} = B^2 = B_1^2 + B_2^2 + B_3^2<\/li>\n<\/ul>\n
    • \u4eee\u306b \\bold{A}\\cdot\\bold{B} = 0 \u3067\u3042\u3063\u3066 \\bold{A} \u304a\u3088\u3073 \\bold{B} \u304c\u96f6\u30d9\u30af\u30c8\u30eb\u3067\u306a\u3044\u306a\u3089 \\bold{A} \u304a\u3088\u3073 \\bold{B} \u306f\u76f4\u4ea4\u3057\u307e\u3059\uff0e<\/li>\n<\/ol>\n