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Math Help - Vector identites question

  1. #1
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    Question Vector identites question

    prove that

    Δ.(ΨΔφ x φΔΨ)=0
    where Δ is delta.
    anybody help plz
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  2. #2
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    Re: Vector identites question

    Hey mathgeni04.

    Hint: Expand all the vectors out in terms of <x,y,z> terms and use the definition of the dot and cross products.
    Thanks from MathGeni04
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  3. #3
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    Re: Vector identites question

    Quote Originally Posted by MathGeni04 View Post
    prove that
    Δ.(ΨΔφ x φΔΨ)=0
    where Δ is delta.
    anybody help plz
    I do not disagree with reply #2 but I do wonder if by \Delta you really mean \nabla  =i \frac{\partial }{{\partial x}} +j \frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}~?

    That is 'nabla' or the del operator. If not what does \Delta mean?
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  4. #4
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    Re: Vector identites question

    \Delta is del operator.
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  5. #5
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    Re: Vector identites question

    Quote Originally Posted by MathGeni04 View Post
    prove that

    Δ.(ΨΔφ x φΔΨ)=0
    where Δ is delta.
    anybody help plz
    I'm confused here. If φ and Ψ are functions then what does the operator x represent if not simple multiplication?
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  6. #6
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    Re: Vector identites question

    So you really mean " \nabla \cdot ((\nabla \psi)\phi \times \psi(\nabla\phi))= 0"?
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  7. #7
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    Re: Vector identites question

    Thanks HallsofIvy. If that were the case then the whole thing makes sense, if it's an actual identity that is.
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