 Solution (source code)

by Codex (@codex,  0)

= Solution

Expanding the <cross product> gives
$$
\boxed{\boldsymbol F\times\boldsymbol G
=\begin{pmatrix}-xz\\-yz\\x^2+y^2\end{pmatrix}.}
$$
Taking its <divergence> component by component,
$$
\boxed{\nabla\cdot(\boldsymbol F\times\boldsymbol G)
=\partial_x(-xz)+\partial_y(-yz)+\partial_z(x^2+y^2)=-2z.}
$$

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