A particle subject to a force $\vec{F}(x,y) = \langle -3 y, 3x \rangle$ moves clockwise along the arc of a circle of radius $4$ centered at the origin, beginning at $(0,4)$ and ending at $(4,0)$.

(a) Find the work done by $\vec{F}$. Be sure you can explain the sign of your answer.
Work =

(b) How much work is done if the particle moves from $(0,4)$ to $(4,0)$ along the circular arc as before, then in a straight line to the origin, and then in a straight line to $(0,4)$? Hint: Sketch this closed path and the vector field.
Work =

(c) Is $\vec{F}$ path-independent? ? Yes No Cannot be determined Be sure you can explain your answer.