VC3.20

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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\,

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