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.

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- 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)

- dumbcow

what does del stand for?

- anonymous

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

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## More answers

- anonymous

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

- 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

- 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

- dumbcow

i'm sure someone can help you

- 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

- anonymous

really that would be awesome!!

- 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.

- 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

- KingGeorge

by my calculations, I get 37.280502

- anonymous

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

- KingGeorge

well dang.

- 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.

- KingGeorge

I would ask about it. Is there any more information that could be relevant?

- anonymous

that's all she wrote, question is as is

- KingGeorge

In that case, I would probably ask your teacher about it.

- anonymous

thank you for your time! It was greatly appreciated.

- anonymous

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

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