Yes, I just tried and it works fine even without the addition of unit vectors and the delta.
My problem is that I cannot take the scaling factors in or out of the derivative.
Perhaps I missed somthing?
I need to prove the identity: \nabla(\vec{A} \times \vec{B})=\vec{B} \bullet(\nabla \times \vec{A}) - \vec{A} \bullet( \nabla \times \vec{B})
I need to prove for an arbitrary coordinate system, meaning I have scaling factors.
The proof should be quite straight forward if you use the levi...
I didn't even look at the third property because the firs and the second don't add up.
In the second as you sadi yourself what you wrote doesn't make sense.
but even more problematic is the fact that the first condition isn't met, and that there is no way to make it work.
As you wrote yourself...