Find $7,9,11$ and $13$

Use Stokes' Theorem to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r).$

$7.$ vec$(F)(x,y,z)=($:$x+y^2,y+z^2,z+x^2$:$),C$ is the positively$-$oriented triangle with vertices $(1,0,0),(0,1,0),(0,0,1).$

$9.$ vec$(F)(x,y,z)=($:$xy,yz,zx$:$),C$ is the boundary of the part of the paraboloid

$z=1-x^2-y^2$ in the $1$ st octant, oriented counterclockwise when viewed from above.

$11($a$).$ vec$(F)(x,y,z)=($:$x^{2}z,x{y}^2,z^2$:$),C$ is the intersection of the plane $x+y+z=1$ and the cylinder $x^2+y^2=9,$ equipped with positive orientation.

$13.$ Let vec$(F)(x,y,z)=($:$-y,x,-2$:$),S$ be the cone $z=\sqrt[\phantom{2}]{x^2+y^2},0z4,$ equipped with downward orientation, and $C$ be the boundary curve of $S.$ Verify Stokes' Theorem by evaluating both ${}_S$curlvec$(F)*dvec(S)$ and ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*d{r}^{}.$