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Math Help - Cross Product Result

  1. #1
    Member iPod's Avatar
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    Cross Product Result

    I have attached the Question.

    Im not sure how to prove this identity, I was thinking maybe giving arbitary vectors?
    Attached Thumbnails Attached Thumbnails Cross Product Result-vector-cross-product.png  
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  2. #2
    TD!
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    Re: Cross Product Result

    If \phi is a function of x, y and z, and I denote \phi_x for \tfrac{\partial \phi}{\partial x} (similar for y and z), then

    \phi \nabla \phi = \phi(\phi_x,\phi_y,\phi_z) = (\phi\phi_x,\phi\phi_y,\phi\phi_z)

    Now all you have to do is calculate the curl of this vector (i.e. nabla 'cross product' this vector); but remember that both \phi and the three partial derivatives are functions of x, y and z.
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