Question

vector cross product identity proof: curl(F x G)=(G.del)F - (F.del)G + F(del.G) - G(del.F)

Answer 1

let F = fxi+fyj+fzk and G = gx i + gy j + gz k

take cross product first, and then take again cross product with Del ... simplify it, you will get the Right Hand side.

PS. this is gonna be ugly.

Answer 2

Yes pretty darn Ugly.
But isn't there a simpler proof? I have tried what you have told.RHS doesn't come up

Answer 3

it does ,,, you have to look for the pattern

Answer 4

this is going to be the ugliest of the ugly. http://upload.wikimedia.org/wikipedia/en/math/b/6/8/b68f5acff7a101d7494bfea654e21c7a.png