# Vector and Tensor problems

1. May 15, 2011

### slashragnarok

Hi guys and gals. I'm stuck on the following problems. Please help me out.

1. Show that curl v is twice the local angular velocity (w), where v is the velocity vector of the fluid.

2. Prove that I:v= div v where I is a unit tensor.

3. Explain why alternating unit tensor is very important in order to describe the cross product of two vectors.

4. If div E=0, div H=0, curl E=- $$\partial$$H/$$\partial$$ t , curl H= $$\partial$$E /$$\partial$$t then show that E and H satisfy $$\nabla$$2u= $$\partial$$2u/$$\partial$$t2

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