\(\vec F = xz^2 \hat i - 2y^2 z^2 \hat j + xy^3z \hat k\)
\(div \,\vec F = \left(\frac{\partial }{\partial x}i + \frac{\partial }{\partial y} \hat j + \frac{\partial }{\partial z} \hat k\right) (xz^2\hat i - 2y^2 z^2 \hat j + xy^3 z\hat k)\)
\(= \frac{\partial }{\partial x}xz^2 + \frac{\partial}{\partial y} (-2y^2 z^2) + \frac{\partial }{\partial z} (xy^3 z)\)
\(= z^2 - 4yz^2 + xy^3\)
\(\therefore (div \,\vec F) (1, 1,-1) = 1 - 4 + 1 = 2 - 4 = -2\)
