## anonymous 4 years ago 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.

1. anonymous

his is using identities involving Grad, Div and Curl as far as i know the identity is shown as : (del)∗(FXG)=((del)crossF)dotG)−Fdot((del)crossG)

2. dumbcow

what does del stand for?

3. anonymous

would delcrossG be zero since G is a constant vector field?

4. anonymous

del is the gradient notation.. the upside down triangle i.e. del cross F is curl of F

5. dumbcow

oh ok like "delta" i never studied vector fields that much so i don't think i can really help you with this question

6. anonymous

ah, okay well thank you anyways, I thought i had it figured but i wasn't able to get an acceptable answer, but i can ask someone tomorrow i guess

7. dumbcow

8. KingGeorge

I found a useful page on wikipedia that may be able to help you. Give me a couple more minutes and I might be able to re-educate myself on this stuff enough to help you also. http://en.wikipedia.org/wiki/Divergence#Properties

9. anonymous

really that would be awesome!!

10. KingGeorge

Well, as best as I can figure out, if G(x, y, z) is constant in the region around G(0) the solution should just be $(-6.914) \cdot (-8.196)+(5.159)\cdot (-1.838) + (4.502) \cdot (-2.2)$But if G isn't constant in that area, I don't think you have enough information. The answer comes from the identity $\text{\div}(F \times G)=\text{Curl}(F) \cdot G - F \cdot \text{Curl}(G)$Since G would be constant, the second term would be 0, leaving us with only the first term.

11. anonymous

thanks a lot! I swear this is correct too, because I had tried this before. I only got lost because the calculated number i came out with was not one of the options on my assignment, so i was wondering where i may have made a mistake, or even if the mistake is in the question or answers themselves

12. KingGeorge

by my calculations, I get 37.280502

13. anonymous

solving i get 37.280502 which sadly is not on my list :(

14. KingGeorge

well dang.

15. anonymous

i know right?! but it wouldn't be the first time they messed up on the question, so perhaps it is worth an ask.

16. KingGeorge

17. anonymous

that's all she wrote, question is as is

18. KingGeorge

19. anonymous

thank you for your time! It was greatly appreciated.

20. anonymous

It's good to know i'm not alone on my train of thought..