Vector differentiations

Question

If A and B are irrotational How to Prove that AxB is solenoidal. Given Ais Irrotational B is irrotational. We have from the prooperties of irrotational vectors that if any vector is irrotational we have div.V equals to zero and there exists a scalar point function phi that F=Del phi So we have 1. A=del phi 2. B =Del Psi

Answer 1

Hint: use the formula $$ {\rm div}(A\times B) = ({\rm curl\ }A)\cdot B - A\cdot({\rm curl\ }B). $$