Let $C$ be the straight path from $(0, 0)$ to $(3, 3)$ and let $\vec F = (y-x - 3)\vec i + ( \sin(y-x) - 3)\vec j$.

(a) At each point of $C$, what angle does $\vec F$ make with a tangent vector to $C$?
angle =
(Give your answer in radians.)

(b) Find the magnitude $\Vert \vec F\Vert$ at each point of $C$.
$\Vert \vec F\Vert =$

Evaluate $\int_C \vec F \cdot d\vec r$.
$\int_C \vec F \cdot d\vec r =$