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Math Help - Cross product and vectors

  1. #1
    Junior Member
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    Cross product and vectors

    "Given that v and w are vectors such that v x w = 2i - j + 3k, find:
    (v + 3w) x (2w - v)"

    My working:
    -> 2(v x w) -3(w x v)

    Having a look at the solution, the equation needs to be further simplified: as 5(v x w) and what I do not understand is how you would be able to get to that equation. I understand the working out from after having simplified the equation - it is just this step of the answer that I am having difficulty with.
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  2. #2
    A Plied Mathematician
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    Note that

    \mathbf{w}\times\mathbf{v}=-\mathbf{v}\times\mathbf{w}.

    That is, I think, the missing piece.
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