Problem $1$: $[15$ points$]$ Do the following forces have a potential energy? If yes calculate it$.$

$($a$)$

vec$(F)=$vec$(F)(x,y,z)=(-3a{y}^2+4bz,-6$axy,$4bx)$

$,$ and

$($b$)$

vec$(F)=$vec$(F)(,,)=$asin$hat()-$bcos$coshat()$

$,$ where a and $b$ are constants.