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Identity for the cross of a curl?

  1. Apr 18, 2012 #1
    Hello! I'm want to prove a vector identity for

    [tex](\nabla \times \vec{A}) \times \vec A[/tex]

    using the familiar method of levi-civita symbols and the identity

    [tex]\epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}[/tex],
    but I don't seem to come up with any usefull answer. I end up with that


    [tex][(\nabla \times \vec{A}) \times \vec A]_k = (\partial_j A_k)A_j - (\partial_k A_j)A_j[/tex]
    , which doesn't seem to reduce something familiar in terms of vectors and vector operators. Any idea how I might get there?
     
  2. jcsd
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