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Using Lagrange Iden. to proof

  1. Jan 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that (A x B) . (u x v) = (a.u) (b.v) - (a.v)(b.u)

    3. The attempt at a solution

    I've used lagrange indentity to proof that. but I can't go ahead

  2. jcsd
  3. Jan 14, 2012 #2


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    Gold Member

    Patience is a virtue here.

    I guess you know already that the LHS equals to:
    det((AxB)1 (AxB)2 (AxB)3 ; u1 u2 u3 ; v1 v2 v3)

    and that (AxB)i= Aj Bk - Ak Bj for a suitable cyclic order.
    Now calculate the determinant.

    afterward calculate explicitly the RHS.

    There's no other way, you need to get your hand dirty.
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