Come on Calculus Friends!! If you are given curl i.e. (del (cross) F) what is the method to figure out what F is, when (del (cross) F) is a vector quantity i.e. (#, #, #)

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Come on Calculus Friends!! If you are given curl i.e. (del (cross) F) what is the method to figure out what F is, when (del (cross) F) is a vector quantity i.e. (#, #, #)

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there isn't an easy way to do it
you've got yourself a lovely set of 3 partial differential equations. \[\frac{\delta u_y}{\delta z}-\frac{\delta u_z}{\delta y}=f(x,y,z) \hat{x}\] etc.
can I show you the actual question and get your opinion on what to do from there?

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yeah, that'd be helpful, cause in general there's not really a set method of doing it that I'm aware of
Let F and G be vector fields such that (del) X F(0) = (-6.914, 5.159, 4.502), G(0) = (-8.196, -1.838, -2.2). Find the divergence of F X G at 0.
as far as i know the identity is shown as : (del)∗(FXG)=((del)crossF)dotG)−Fdot((del)crossG)
ah, okay, this is a bit of a trick, the divergence of a curl is always zero.
Ha! problem solved
oh wait, nvm, that wasnt in the question...
well the second part it kind of is no?
no, its the dot product with a curl, its different.
hmm..
so you are saying that F(dot)[del(cross)G) is not.. a divergence of a curl?
I guess, yeah that wouldn't make much sense, because then why would they have that identity in the first place
.. if it was just zero
yeah, g(0) is all constants though, shouldnt the curl of it be zero?
so all you'll have is the dot product of the two? I could be wrong, but from what I see you're definitly not given enough information to reverse engineer the field for f out of what you have
See, those are the types of things i'm still trying to grasp.. aha. it would be nice make things much easier
okay then that must be the best bet, I have possible answers, so i'll try and if I get it I'll let you know either way. thank you for your help!
k, best of luck

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