Div(curl(F)) = 0, understanding its meaning.

[flyingpig]

Homework Statement

Is there a vector field F on R³ such that curlG = <xy²,yz², zx²>?

The Attempt at a Solution

div(curl(G)) ≠ 0, so no, G is not a vector field.

Now my question is, does this conclude any thing about G? does that mean G is a scalar field?

If by some chance that div(curl(G)) = 0, does that mean G is also a conservative field?

 

[Matterwave]

Curl only acts on vector fields. Since div(curl(G)) is not 0, we can conclude that G does not exist. In other words, there is no way you can get a curl of something to have a divergence.