Consider vec$(F)=(cosx)vec(i)+e^y$vec$(j)+(4x-4y-3z)vec(k).$

$($a$)$ Find curl vec$(F).$

curlvec$(F)=$ vec$(i)+$

$$ vec$(k)$

$($b$)$ Find ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ where $C$ is the circle of radius $3$ in the plane $x+y+z=1,$ centered at $(1,0,0)$ oriented counterclockwise when viewed from above.

NOTE: Enter the exact answer, or round to three decimal places. ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$