$(2)$ Compute $,{\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ given vec$(F)(x,y,z)=($:$yz,x,z^2$:$)$ and C is the intersection of the paraboloid $z=x^2{y}^2$ and the sphere $x^2{y}^2{z}^2=6,$ oriented in the positive direction