Answer
The vector field $F$ is in-compressible.
Work Step by Step
Let us consider $F=ai+b j+c k$
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}$
Now, $div F= \nabla \cdot F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
or, $\nabla \cdot F=[\dfrac{\partial i}{\partial x}+\dfrac{\partial j}{\partial y}+\dfrac{\partial k}{\partial z}] \cdot (f(y,z) i+g(x,z) j+h(x,y) i=0$
Hence, the vector field $F$ is in-compressible.
