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Prove (u+v) x (u-v) = 2v x u (Cross product)

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that (u+v) x (u-v) = 2v x u

    2. Relevant equations

    being u=(x1,y1,z1)
    and v= u=(x2,y2,z2)

    3. The attempt at a solution

    I've got 2v x u equals:

    (2y2.z1 - 2z2.y1) + (2x2.z1 - 2z2.x1) +
    (2x2.y1 - 2y2.x1)

    But I'm nearly to melt my mind to prove (u+v) x (u-v) = above
    Last edited: May 21, 2012
  2. jcsd
  3. May 21, 2012 #2


    User Avatar
    Homework Helper

    Expand the product, and use that property of the cross product that uxv=-vxu and the product of identical vectors is zero.

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