Given Vector Field F =<yz,xz,yz^2-y^2z>, find VF's A and B such that F=Curl(A)=Curl(B) and B-A is nonconstant

Question

Given Vector Field F =, find VF's A and B such that F=Curl(A)=Curl(B) and B-A is nonconstant

I already showed that Div(F)=0 but finding two new VF's with that property is difficult,.. especially if I have no idea where to start.

Answer 1

Hint:

Start by using definition of curl. i.e

$F = (yz,xz,yz^2-y^2z) = \nabla \times A = (\frac{\partial A_3 }{\partial y}-\frac{\partial A_2}{\partial z}, \frac{\partial A_1}{\partial z}-\frac{\partial A_3}{\partial x}, \frac{\partial A_2}{\partial x}-\frac{\partial A_1}{\partial y})$ Solving this PDE.