Answer
a) $0$
b) $y^2z^2+x^2z^2+x^2y^2$
Work Step by Step
a) Consider $F=A i+B j+C k$
Then $curl F=\begin{vmatrix}i&j&k\\\dfrac{\partial}{\partial x}&\dfrac{\partial }{\partial y}&\dfrac{\partial }{\partial z}\\A&B&C\end{vmatrix}$
$curl F=[C_y-B_z]i+[A_z-C_z]j+[B_x-A_y]k$
$curl F=[2x^2yz-2x^2yz]i+[2xy^2z-2xy^2z]j+[2xyz^2-2xyz^2]k=0$
b) $div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
$div F=\dfrac{\partial (xy^2z^2)}{\partial x}+\dfrac{\partial (x^2yz^2)}{\partial y}+\dfrac{\partial (x^2y^2z)}{\partial z}=y^2z^2+x^2z^2+x^2y^2$
