## anonymous 4 years ago 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. (#, #, #)

1. anonymous

there isn't an easy way to do it

2. anonymous

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.

3. anonymous

can I show you the actual question and get your opinion on what to do from there?

4. anonymous

yeah, that'd be helpful, cause in general there's not really a set method of doing it that I'm aware of

5. anonymous

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.

6. anonymous

as far as i know the identity is shown as : (del)∗(FXG)=((del)crossF)dotG)−Fdot((del)crossG)

7. anonymous

ah, okay, this is a bit of a trick, the divergence of a curl is always zero.

8. anonymous

Ha! problem solved

9. anonymous

oh wait, nvm, that wasnt in the question...

10. anonymous

well the second part it kind of is no?

11. anonymous

no, its the dot product with a curl, its different.

12. anonymous

hmm..

13. anonymous

so you are saying that F(dot)[del(cross)G) is not.. a divergence of a curl?

14. anonymous

I guess, yeah that wouldn't make much sense, because then why would they have that identity in the first place

15. anonymous

.. if it was just zero

16. anonymous

yeah, g(0) is all constants though, shouldnt the curl of it be zero?

17. anonymous

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

18. anonymous

See, those are the types of things i'm still trying to grasp.. aha. it would be nice make things much easier

19. anonymous

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!

20. anonymous

k, best of luck