The two components $($in $x$ and $y$ directions$)$ of the velocity in a $3$D incompressible flow field are given by:

$u=x^2+y^2+z^2$

$v=2xy+yz+z^2$

$($a$).$ Determine the velocity component $w,$ that is in the $z$ direction.

$($b$).$ Is this flow rotational or irrotational? Justify your answer with necessary calculations.