Answer
There is no such vector field $G$.
Work Step by Step
Let us consider $F=ai+bj+ck$
Then, $ div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}$
The div (curl G) must be zero when there exist a vector field $G$ for all values of $x,y$ and $z$.
Given: $curlG=2x i+3y z j-xz^2 k$
Thus,
$ div (curl G)=\dfrac{\partial (2x)}{\partial x}+\dfrac{\partial (3yz)}{\partial y}+\dfrac{\partial (-xz^2)}{\partial z}$
or, $=-2+3z-2xz$
It has been proved that there is div (curl G) is not zero, there is no vector field $G$.
