vector analysis problem

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November 17th 2009, 09:09 AM
ntfabolous

vector analysis problem

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

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$\vec{v}\cdot\nabla\vec{v}=\frac{1}{2}\nabla(\vec{v }\cdot\vec{v})-(\vec{v}\times(\nabla\times\vec{v}))$
November 17th 2009, 08:50 PM
qmech

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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