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Math Help - vector analysis problem

  1. #1
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    Sep 2009
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    Lightbulb vector analysis problem

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

    Show that

    \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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    Thanks
    2

    Useful vector identity

    Try using the identity:
    {{\nabla}} <br />
(\vec A\cdot \vec B)<br />
=<br />
(\vec A\cdot {{\nabla}})\vec B +<br />
(\vec B\cdot {{\nabla}})\vec A +<br />
\vec A\times ({{\nabla}} \times\vec B) +<br />
\vec B\times ({{\nabla}} \times\vec A)<br /> <br />
    and substitute in your v for A and B.
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