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# I need help on this vector calculus question... watch

1. Prove that if f is a (smooth) scalar field and G is an irrotational vector field, then
(∇f × G )f is solenoidal

Ive got the identities in front of me but i dont know how to apply them to this question.

Any help will be appreciated
2. (Original post by TeeEm)
Irrotational means curl is zero
solenoidal means divergence is zero

Take the divergence of
(f× G )f
and see what happens
would taking the divergance mean that
(f× G )f =0 and work from there??
3. (Original post by TeeEm)
Yes
I do not remember right now all the vector identities, but there would be curlG also appearing in the proof which of course they would be zero
∇ · (fG ) = (∇f) · G + f∇ · G

∇ · (F×G ) = (∇ × F )·G − F· (∇ × G )
Ive gone through all of my identities and picked these 2 out that can solve this. Are these 2 suitable for this question??

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