Solution:

$\bar A = x^{2} z \bar i -2y^{2} z^{2} \bar j + xy^{2} z \bar k $

The divergence of $\bar A$ is given by

$\nabla. \bar A = \frac{\partial A_x}{\partial x} + \frac{\partial A_y}{\partial y} + \frac{\partial A_z}{\partial z}$

$\begin{aligned} \frac{\partial A_x}{\partial x} &= 2xz \\ \frac{\partial A_y}{\partial …