Answer
$0$
Work Step by Step
As we know that $div F=\dfrac{\partial A}{\partial x}i+\dfrac{\partial B}{\partial y}j+\dfrac{\partial C}{\partial z}k$
Now, we have
$div F=\dfrac{\partial}{\partial x}[0]+\dfrac{\partial}{\partial y} [0]+\dfrac{\partial}{\partial z} [(a^2-x^2-y^2)]$
This implies that
$div F=0$
