I do not understand this vector identity proof

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SUMMARY

The discussion centers on understanding vector identities, specifically the proof involving the curl of the cross product of two vector fields A and B. The user struggles with the notation and operations, particularly the meaning of "F times nabla" and its relation to divergence. The correct formulation includes terms like -(G*Nabla)*F, and the user ultimately confirms that their answer aligns with the professor's, despite initial confusion regarding the conversion of summations to vector quantities.

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  • Understanding of vector calculus concepts, including curl and divergence.
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Xyius
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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.
 
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u know, i have done the above proof, i.e,
curl of (A χ B)
but it came out to be (B .[itex]\nabla[/itex])A-B([itex]\nabla[/itex] . A)-(A.[itex]\nabla[/itex]) B+ A ([itex]\nabla[/itex] . 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.
 
I got my answer to be his answer. My main confusion was linking the formulas to the vector operation in the last step.
 

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