Curl and Divergence (flux, and what not)

[dink]

I'm having a bit of difficulty with this problem:
<br /> \vec{\nabla} \times \vec{G} = \vec{F}<br />
where
\vec{\nabla} \cdot \vec{F} = 0
and \vec{F} = &lt;y, z, x&gt;.
Find \vec{G}. I'm really at a loss how to solve this. I know the solution must be quick and easy because it was on a quiz. What I do know is this is called "incompressable" if, say it were a vector field of a fluid. Any help would be appreciated.

 

[James R]

You have:

\vec{\nabla}.(\vec{\nabla} \times \vec{G}) = 0

Can you expand the left hand side using a suitable vector identity?

 

[dink]

http://astron.berkeley.edu/~jrg/ay202/node189.html ?

14.54 gives me the form, such that A = G, but does this mean B = F if I expanded to 14.51?

 

[dink]

Just a follow up incase someone else needed the same solution. Merely expanding the cross product (<P,Q,R> form as \vec{G}) leaves a vector in differentials that is equal to \vec{F}. From then its just a matter of setting the components equal to each other and knocking off which ever differential you would like. You can do this because the solution is not unique. Thanks for the help.