1. The problem statement, all variables and given/known data A vector field F for which div F = 0, is called incompressible (also called solenoidal). Consider the vector field F(x, y, z) = ⟨y, x + y, −z⟩. (a) (1 point) Show that F is incompressible. (b) (3 points) Find a vector field A such that F=[tex]\nabla[/tex]×A. 2. Relevant equations div F = [tex]\nabla[/tex] . F 3. The attempt at a solution I understand how to do part a and confirmed that div F = 0 and thus is incompressible. But I'm not entirely sure how to find part b. Is there a cross product operation in which A = some combination of F and [tex]\nabla[/tex]? Or would you assign A some arbitrary vectors [tex]\left\langle[/tex]P,Q,R⟩ and take the cross of those with [tex]\nabla[/tex]. Resulting in the vector ⟨y, x + y, −z⟩ = (dR/dy-dQ/dz)i-(dR/dx-dP/dz)j+(dQ/dx-dP/dy)k and somehow solve for P,Q,R? Or am I completely on the wrong track? Any help or advice would be wonderful!