Answer
Conservative
Work Step by Step
A vector field is said to be conservative when $ curl \space F=\nabla \times F=0$
Thus, $$ curl \space F= \nabla \times F=(\dfrac{\partial z}{\partial y}-\dfrac{\partial y}{\partial z}) \space i+(\dfrac{\partial x}{\partial z}-\dfrac{\partial z}{\partial x}) \space j+(\dfrac{\partial y}{\partial x}-\dfrac{\partial x}{\partial y}) \space k $$
From the given equation, we have
$ curl F=(0-0)i+(0-0)j+(0-0) k=0$
Thus, the given field $ F $ is conservative.
