$[5]($a$)$ Force of vec$(F)=7$hat$(i)+4$hat$(j)($unit $N)$ is applied to displacement of $vec(r)=3$hat$(i)-4$hat$(j)+2$hat$(k)($unit m$).$ Find work $($unit J$).$

$($b$)$ A particle of mass $m=2kg$ moves in the $xy$ plane with a velocity of vec$(v)=3$hat$(i)+5$hat$(j)($unit $\frac{m}{s}).$ Determine the angular momentum of the particle about the origin when its position vector is vec$(r)=2$hat$(i)+3$hat$(j)($unit $m)$