$(a)$ Determine which $of$ the following vector fields $is$ a curl. $IfFis$ a curl vector field, find $G$ such that $F=$grad$G.$

$(i)F=(x,y,z)$

$(ii)F=(x^2-1,z-2xy,y)$

$(b)$ Consider the vector field

$F(x)=\frac{x}{||x|{|}^3}$

$on\frac{R^3}{\frac{?}{?}}\{(0,0,0)\}.$ Show that div$(F)=0,$ but $F$curl$(G)$ for any $C^1$ vector field $G.$