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Question about the Triple Product

  1. May 30, 2017 #1
    1. The problem statement, all variables and given/known data

    upload_2017-5-30_15-44-59.png



    2. Relevant equations
    a⋅(b x a) = 0

    3. The attempt at a solution

    Is my working below correct? In particular, can you apply the rCB to both the first part of the bracket (0.2j) and the second part (w x rCB) individually like that?

    upload_2017-5-30_15-45-17.png


    My second question relates to:

    upload_2017-5-30_15-45-30.png

    Is that correct? Does it matter if rCB is multiplied at the end or start? I am inclined to think it doesn't as it's a dot product?
     
  2. jcsd
  3. May 30, 2017 #2

    fresh_42

    Staff: Mentor

    Both are correct. The first because the dot product is (bi-)linear, the second, because it is symmetric.
    For the third term to equal zero, you can use the identity ##(\vec{a}\times \vec{b}) \cdot \vec{c} = (\vec{b}\times \vec{c}) \cdot \vec{a} = (\vec{c}\times \vec{a}) \cdot \vec{b}## and the anti-symmetry of the cross product: ##\vec{a}\times \vec{a} = \vec{0}##.
     
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