Is there some formula for the Divergence of cross Product of (n-1) vectors in $\mathbb{R}_n$. I happen to know of such a formula for $\mathbb{R}_3$, so wanted to know. Pls add/link a proof as well.
Here is the three dimensional case. $\vec{\nabla} \cdot\left ( \vec{A}\times\vec{B} \right )=\vec{B}\cdot\left ( \nabla \times\vec{A} \right )-\vec{A}\cdot\left ( \nabla \times\vec{B} \right )$