A vector field is called irrotational if its curl is zero. A vector field is called solenoidal if its divergence is zero. If A and B are irrotational, prove that A $ \times $ B is solenoidal.
I'm having a hard time the proof equation that is required, and the steps that would go with it. I am defining V as a vector.
$ \nabla \times V = 0 $ = irrotational
$ \nabla \cdot V = 0 $ = solenoidal
$ \nabla \times A = 0 $
$ \nabla \times B = 0 $
so therefore, ($ \nabla \times A $)+ ($ \nabla \times B) = \nabla \cdot (A \times B) $
would this be a correct setup? I'm having a hard time expanding this to E.S. form.