Vector and Tensor problems

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=- [tex]\partial[/tex]H/[tex]\partial[/tex] t , curl H= [tex]\partial[/tex]E /[tex]\partial[/tex]t then show that E and H satisfy [tex]\nabla[/tex]²u= [tex]\partial[/tex]²u/[tex]\partial[/tex]t²