## Index notation help please (sorry if in wrong section)

After spending hours trying to understand the basic points of index notation, I have failed miserably. I will be getting a library book tomorrow, but as I have a few questions in for tomorrow, any help would be very appreciated.

1) Write the following in index notation:

grad x (fu) [u vector, f scalar]

2) Use index notation to prove the following identities:

grad . (u x v) = (grad x u) . v - (grad x v) . u

3) Show using index notation that for an arbitrary vector field u:

u x (grad x u) = grad (1/2 u^2) - (u . grad)u [where u^2 = u.u]

Hence, or otherwise show that for a vector field u for which grad x u is parallel to u that: