Let $u=($:$-1,3$:$)$ and $v=($:$-4,2$:$).$

$($a$)$ Calculate $2u-\frac{1}{2}v,$ and sketch it in the plane.

$($b$)$ Find a unit vector pointing in the same direction as $u.$

$($c$)$ Find a vector of length $3$ parallel to $v$ but pointing in the opposite direction.