Thread: vector analysis problem

1. vector analysis problem

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

Show that

$\vec{v}\cdot\nabla\vec{v}=\frac{1}{2}\nabla(\vec{v }\cdot\vec{v})-(\vec{v}\times(\nabla\times\vec{v}))$

2. Useful vector identity

Try using the identity:
${{\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.