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Thread: vector analysis problem

  1. #1
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    Lightbulb vector analysis problem

    Hello, I need help here for my hw. Help will be appreciated!

    Show that

    $\displaystyle \vec{v}\cdot\nabla\vec{v}=\frac{1}{2}\nabla(\vec{v }\cdot\vec{v})-(\vec{v}\times(\nabla\times\vec{v}))$
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  2. #2
    Senior Member
    Joined
    Nov 2009
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    2

    Useful vector identity

    Try using the identity:
    $\displaystyle {{\nabla}}
    (\vec A\cdot \vec B)
    =
    (\vec A\cdot {{\nabla}})\vec B +
    (\vec B\cdot {{\nabla}})\vec A +
    \vec A\times ({{\nabla}} \times\vec B) +
    \vec B\times ({{\nabla}} \times\vec A)

    $
    and substitute in your v for A and B.
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