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

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    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
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    (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??
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    (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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