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Vector Analysis Homework

  1. Feb 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that an arbitrary vector V can be expressed in terms of any three noncoplanar vectors, A, B, C, according to:

    V = [V,B,C]A/[A,B,C] + [V,C,A]B/[A,B,C] + [V,A,B]C/[A,B,C]


    2. Relevant equations
    A Hint is given:
    We know that V can be expressed as aA + bB +cC; to find a, take the scalar product of V with BxC


    3. The attempt at a solution
    I tried to solve this one by relating the projections of V to 3 arbitrary vectors, A, B, C, but I couldn't get to the answer above. I'm also not sure how the hint will help me either. Could someone please help me get started on this because Im all out of ideas.

    thanks
     
  2. jcsd
  3. Feb 3, 2008 #2

    Dick

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    I'm assuming [V,B,C] is the triple product V.(BxC), right? Then what is [V,B,C]? It's (aA+bB+cC).(BxC). BxC is perpendicular to B and C, so those parts of the dot product are zero. This leaves you with [V,B,C]=aA.(BxC)=a*[A,B,C]. Put that into your formula and treat the other two terms the same way.
     
  4. Feb 3, 2008 #3
    Wow, so the hint gave it away -- i cant believe i didn't see that. Thanks a lot for the help though!
     
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