Re: [微積]Vector Triple Product A ×(B ×C ) 證明

[Honor1984 (奈何上天造化弄人？)]

藥用幾何的方式就要辛苦一點

B、C展開平面E，設A對E的投影向量A'

C沿著B及垂直B的方向分解為C"及C'

其中C' = C - B(C * B)/|B|^2

    C" = B(C * B)/|B|^2

A x (B x C)

= A' x (B x C')

= [B(A * B)/|B|^2 + C'(A * C')/|C'|^2] x (B x C')

= -(A * B)C' + (A * C')B

= -(A * B)(C - C") + [A * (C - C")]B

= -C(A * B) + B(A * C) + C"(A * B) - B(A * C")

= -C(A * B) + B(A * C)

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→ Honor1984   : 第一個字就錯了，藥=>要