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Thread: Cross Product Result

  1. #1
    Member iPod's Avatar
    Jul 2009

    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! is offline
    Senior Member
    Jan 2006
    Brussels, Belgium

    Re: Cross Product Result

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

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

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