Let $\vec F = 2 y\vec i + 3 x\vec j$, $\phi = 2 x^3 + 2 x y$, and $h = y - 3 x^2$.

(a) Find each of the following:
$\vec F - \nabla \phi =$
$\nabla h =$
How are $\vec F - \nabla \phi$ and $\nabla h$ related?
$\vec F - \nabla \phi =$ $\nabla h$
(Note that this shows that $\vec F - \nabla \phi$ is parallel to $\nabla h$.)

(b) Use $\phi$ and the Fundamental Theorem of Calculus for Line Integrals to evaluate $\int_C \vec F\cdot d\vec r$, where $C$ is the oriented path on a contour of $h$ from $P(0,2)$ to $Q(5,77)$.
$\int_C \vec F\cdot d\vec r =$