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Lagrange Triple Vector proof

  1. Sep 9, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]a \times (b \times c) = (a * c)b - (a*b)c[/tex]

    For orthagonal coordinates, a,b,c

    2. Relevant equations

    Cross Product and Dot Product

    3. The attempt at a solution

    I thought about expanding both sides out and proving they are equal, but I just realized that the left side of the theorem would give me a vector and the right side would give me a scalar. Perhaps I don't understand the theorem perfectly. Can someone explain the notion about this theorem and how I would go about proving it?
  2. jcsd
  3. Sep 9, 2008 #2
    I should clarify a bit

    a,b,c are for cartesian orthagonal coordinates (i,j,k vectors are all normal to each other)
  4. Sep 9, 2008 #3


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    If a,b and c are vectors the right side IS a vector. (a.c)b-(a.c)c is scalar*vector minus scalar*vector. It's a vector. And you can just multiply it out.
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