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Vector Triple Production Reduction

  1. Sep 9, 2011 #1
    [itex]\nabla[/itex]x (A x B)
    I'm trying to reduce this triple product down so nabla is only operating on either A or B, not the product of the two vectors.

    I've been playing with this for a while now but can't really seem to make a dent in it. Any suggestions would be well appreciated.
     
  2. jcsd
  3. Sep 9, 2011 #2
    There's a pretty famous relation:

    [itex]\nabla\times(\nabla\times\vec{F}) = \nabla(\nabla \cdot F) - \nabla^{2}F[/itex] =
    = grad(div(F)) - Laplacian(F)

    Proof can be of course rigorously done either through actual component calculation or using other relations, but I believe you can just use this :-)
     
    Last edited: Sep 9, 2011
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