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Homework Help: Scalar triple product

  1. Aug 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that
    (A X B) X C = AxBxCx (i x k) + AyBxCy (j x k)
    where i , j and k are unit vectors ?

    2. Relevant equations

    3. The attempt at a solution

    let A= Axi+Ayj
    B= Bxi+Byj

    L.H.S = (AXB)XC
    = (C.A) B - (C.B) A
    = (AxCx+AyCy)(Bxi+Byj)- (BxCx+ByCy)(Axi+Ayj)
    after simplification we get
    = AxByCx i - AxByCy j + AyBxCy i - AyBxCx j
    there i am held up.... now how i proceed further..
  2. jcsd
  3. Aug 19, 2010 #2
    I believe you should start by writing A and B has 3 dimensional vectors rather than 2. I would follow the exact steps you have above and then finish the problem by expanding the RHS (AxBxCx (i x k) + AyBxCy (j x k)) and showing that the two are equivalent.
  4. Aug 19, 2010 #3


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    It doesn't work for A=i, B=j, and C=i. Since Bx=0, the righthand side is equal to 0, but the lefthand side is equal to j.
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