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Vector cross Product

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data

    C= B|A| + A|B|
    D= A|B|-B|A|
    C and D are orthogonal
    Find a third vector perpendicular to both C and D

    2. Relevant equations

    [AxB] = |A||B|sin(theta)

    3. The attempt at a solution

    I know that to find the answer I need to find the cross product of C and D. I have done similar problems, but the unit components (i,j,k) have always been given. I can't figure out a way to do this without having those.
    Thanks for any help, even a hint!
  2. jcsd
  3. Jan 26, 2010 #2


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    CXD = (B|A| + A|B|)X( A|B|-B|A|)
    Do the cross multiplication of right hand side. Note that AXA = BXB = 0 And AXB = -BXA
    You can multiply the magnitudes of A and B directly.
  4. Jan 26, 2010 #3
    so I can do...

    BxA|A||B| + BxB|A||A| + AxA|B||B| - AxB|B||A|
    BxA|A||B| - AxB|B||A|

    so would that be the final answer? thanks for the help, this all just seems a little weird to me. I didnt know that you could just essentially "foil" it like that
  5. Jan 26, 2010 #4


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    Last step
    CXD = 2(AB)*BXA, because AXB = BXB = 0
  6. Jan 26, 2010 #5
    thanks, you're a lifesaver! i totally get it now
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