Let $C$ be the straight path from $(0,0)$ to $(6,6)$ and let vec$(F)=(y-x+4)vec(i)+(sin(y-x)+4)vec(j).$

$($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 $||vec(F)||$ at each point of $C.$

$||vec(F)||=$

Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r).$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$