Question

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.

Answer 1

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)

Answer 2

what does del stand for?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

i'm sure someone can help you

Answer 8

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

Answer 9

really that would be awesome!!

Answer 10

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.

Answer 11

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

Answer 12

by my calculations, I get 37.280502

Answer 13

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

Answer 14

well dang.

Answer 15

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

Answer 16

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

Answer 17

that's all she wrote, question is as is

Answer 18

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

Answer 19

thank you for your time! It was greatly appreciated.

Answer 20

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