c) Compute $\oint_{C} F \cdot d r$ where $\mathrm{C}$ is the circle of radius 2 centered at $(0,1,3)$ in the plane $x+2 y+3 z=11$

Step 1 ：Compute \(\oint_{C} F \cdot d r\) where \(\mathrm{C}\) is the circle of radius 2 centered at \((0,1,3)\) in the plane \(x+2 y+3 z=11\)

Step 2 ：The question does not provide enough information to compute the line integral. We need to know the vector field F.

Step 3 ：\(\boxed{\text{The question does not provide enough information to compute the line integral. We need to know the vector field F.}}\)