# VC3.20

Curl of the given vector is $\mathrm{curl}V=\begin{vmatrix} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ (x^2+yz) & (y^2+zx) & (z^2+xy)\end{vmatrix}\,$
=$[\frac{\partial}{\partial y}(z^2+xy)-\frac{\partial}{\partial z}(y^2+zx)]i-[\frac{\partial}{\partial x}(z^2+xy)-\frac{\partial}{\partial z}(x^2+yz)]j+[\frac{\partial}{\partial x}(y^2+zx)-\frac{\partial}{\partial y}(x^2+yz)]k\,$
=$(x-x)i-(y-y)j+(z-z)k=0\,$