= Solution
Using $r=(x,y,z)$ and constant $a$, the <divergence> is
$$
\partial_i(\epsilon_{ijk}r_ja_k)=\epsilon_{ijk}\delta_{ij}a_k=0.
$$
For the <curl>, the <curl of a cross product> identity gives
$$
\nabla\times(r\times a)=r(\nabla\cdot a)-a(\nabla\cdot r)+(a\cdot\nabla)r-(r\cdot\nabla)a
=0-3a+a-0.
$$
Thus
$$
\boxed{\nabla\cdot(r\times a)=0,\qquad\nabla\times(r\times a)=-2a.}
$$
For a quick sign check, taking $a=e_z$ gives $r\times a=(y,-x,0)$, whose <curl> is $(0,0,-2)$.
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