$($i$)$ Consider a vector field $v$ defined as

$v=x^{2}zi+2y^3{z}^{2}j+xy{z}^{2}k$

Determine the divergence of this vector field.

$($ii$)$ Show that the vector field

$v=xsinyi+ysinxj-z(sinx+siny)k$

is solenoidal.