Answer
a) 0
b) $y^2z^2+x^2z^2+x^2y^2$
Work Step by Step
a) When $F=ai+bj+ck$, then we have $curl F=[c_y-b_z]i+[a_z-c_z]j+[b_x-a_y]k$
$curl F=[2x^2yz-2x^2yz]i+[2xy^2z-2xy^2z]j+[2xyz^2-2xyz^2]k=0$
b) $div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}=\dfrac{\partial (xy^2z^2)}{\partial x}+\dfrac{\partial (x^2yz^2)}{\partial y}+\dfrac{\partial (x^2y^2z)}{\partial z}=y^2z^2+x^2z^2+x^2y^2$
