A circle $C$ in the plane $x+y+z=3$ has a radius of $5$ and center $(3,1,-1).$ Evaluate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ for $F=($:$0,-3z,4y$:$),$ where $C$ has counterclockwise orientation when viewed from above. Does the circulation the circle? Does it depend on the location of the center of the circle?

$o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr=$

$$

$($Type an exact answer, using $$ as needed.$)$

Does the circulation depend on the radius of the circle?

A$.$ Yes. The circulation is inversely proportional to the square of the radius.

B$.$ Yes. The circulation is inversely proportional to the radius.

C$.$ No$.$ The circulation does not change with the radius.

D$.$ Yes. The circulation is proportional to the radius.

E$.$ Yes. The circulation is proportional to the square of the radius.

Does the circulation depend on the location of the center of the circle?

A$.$ No$.$ The circulation does not change when the circle moves in the plane.

B$.$ Yes. The circulation has a complex relationship with the location of the circle.

C$.$ Yes. The circulation changes linearly with $y.$

n Vec The rirculation shannec linearly with $x$