= Solution
The <vector calculus identity> $\nabla\cdot(\mathbf A\times\mathbf B)=\mathbf B\cdot(\nabla\times\mathbf A)-\mathbf A\cdot(\nabla\times\mathbf B)$ gives zero because a constant <vector field> has zero <curl> and $\nabla\times\mathbf r=0$. Thus
$$
\boxed{\nabla\cdot(\mathbf a\times\mathbf r)=0.}
$$
Equivalently, the Cartesian components are $(a_yz-a_zy,a_zx-a_xz,a_xy-a_yx)$, and each component is independent of the coordinate used in its contribution to the <divergence>.
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