I do not understand this vector identity proof

[Xyius]

So I am trying to follow my professors notes. Here is my work on the proof. And on the bottom is my answer and his answer. I know my answer is wrong, as I do not fully understand how to convert the summations at the end to their vector quantities. Is my work incorrect?

[PLAIN]http://img256.imageshack.us/img256/6175/questionn.gif

I do not even know what F times nabla means. I know nabla times F is divergence. Are they the same?

EDIT: Oh and his G is my q.

AND his answer has a -(G*Nabla)*F at the end.

 

[pari777]

u know, i have done the above proof, i.e,
curl of (A χ B)
but it came out to be (B .\nabla)A-B(\nabla . A)-(A.\nabla) B+ A (\nabla . B)

u see, i am just a beginner in this topic, and i didn't do it like u did it. instead i broke it down all the way and did it. I know it is stupid but i was not so sure so... but i did check the answer and it was correct.

 

[Xyius]

I got my answer to be his answer. My main confusion was linking the formulas to the vector operation in the last step.