Question for final(vector field)

[yzc717]

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My thought on problem#2: if f is scalar function, then this statement would be false?? Does this surface has to be a closed surface?

My thought on problem #3: use Stoke's theorem? omega has to be no boundary?

And I have no idea on the rest of it.

 

[gabbagabbahey]

Is this for a take home final? If so, are you sure you are allowed to seek help in this manner for your test?

As a hint for problem 1, what is the divergence of the curl of any vector field?