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Vector Identity Proof

  1. Oct 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that:
    ∇×(a∙∇a) = a∙∇(∇×a) + (∇∙a)(∇×a) - (∇×a)∙∇a


    2. Relevant equations

    Related to the vorticity transport equation.


    3. The attempt at a solution

    Brand new to index/tensor notation, any suggestions on where to begin? For example, I am having trouble converting to index notation with differentials inside the curl on the LHS.
     
  2. jcsd
  3. Oct 4, 2012 #2

    tiny-tim

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    welcome to pf!

    hi aanabtawi! welcome to pf! :smile:

    (have a curly d: ∂ and try using the X2 button just above the Reply box :wink:)
    write the LHS out carefully with index notation, then use the product rule for derivatives …

    show us how far you get :smile:
     
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