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Math Help - Vector Proof

  1. #1
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    Vector Proof

    If a and b are arbitrary scalar fields, show that

    del.[del(a)xdel(b)] = 0.

    Is this anything to do with perpendicular vectors as I remember if two vectors are indeed perp., then the dot product of both of them equals 0. Or is something totally different here?

    del = operator which looks like an upside triangle
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  2. #2
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    The del operator is defined as \nabla  = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}.
    If each of a & b is a scalar field then \nabla a = a_x i + a_y j + a_z k\quad \& \quad \nabla b = b_x i + b_y j + b_z k.
    \nabla  \cdot \left( {\nabla a \times \nabla b} \right) = \nabla b \cdot \left( {\nabla  \times \nabla a} \right) - \nabla a \cdot \left( {\nabla  \times \nabla b} \right)
    Last edited by Plato; February 27th 2008 at 02:06 PM.
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  3. #3
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    Will that suffice in answering the question? Or do I need to go further?
    Last edited by Yerobi; February 27th 2008 at 03:03 PM.
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  4. #4
    Aralus
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    That should suffice I think...
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