Answer
The vector field $F$ is in-compressible.
Work Step by Step
Let us consider that $F=A i+B j+C k$
$div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
Given: $F(x,y,z)=f(x) i+g(y) j+h(z) k$
Here, we have $div F= \nabla \cdot F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
and $div F= \nabla \cdot F=\dfrac{\partial i}{\partial x}+\dfrac{\partial j}{\partial y}+\dfrac{\partial k}{\partial z} \cdot (f(y,z) i+g(x,z) j+h(x,y) i=0$
Hence, we can see that the vector field $F$ is in-compressible.
