Let curl vec$(F)=-$xvec$(i)+3$vec$(j)+5$zvec$(k),$ let $P=(4,3,4),$ and let $C$ be the circle of radius $0\mathrm{.}005$ centered at $P$ in the plane $x+y+z=11,$ oriented clockwise when viewed from the origin.

$($a$)$ Find curl vec$(F)*(vec(i)+$vec$(j)+$vec$(k))$ at $P.$

curlvec$(F)*(vec(i)+$vec$(j)+$vec$(k))=$

$($b$)$ Use your answer to part $($a$)$ to estimate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r).$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$~~