I need to prove the identity div (a x b) = b dot (curl a) - a dot (curl b)
The Attempt at a Solution
I've done the proof about 10 times now, and everytime I get the left hand of the identity equal to this:
(all the d's are partial derivatives)
d(a3b1)/dx - d(a2b1)/dx + d(a3b1)/dy - d(a1b3)/dy + d(a1b2)/dz - d(a2b1)/dz
where vector a = a1i + a2j + a3k and vector b = b1i + b2j + b3k
When I do the right hand side I get exactly the same thing above but doubled. So in affect I'm deriving 1 = 2. I'm sure there is an easy identity to manipulate the cross and dot products, but the brute force method should work and it's not, and I'm am completely lost as to where.