Let $\vec r=x\,\vec i+y\,\vec j+z\,\vec k$ and $\vec a = 2\,\vec i + 5\,\vec j + 2\,\vec k$.

(a) Find $\nabla (\vec r\cdot \vec a)$.
$\nabla (\vec r\cdot \vec a) =$

(b) Let $C$ be a path from the origin to the point with position vector $\vec{r_0} = a\,\vec i + b\,\vec j + c\,\vec k$. Find $\int_C\nabla(\vec r\cdot\vec a)\cdot d\vec r$.
$\int_C\nabla(\vec r\cdot\vec a)\cdot d\vec r =$

(c) If $\|\vec r_0\|=18$, what is the maximum possible value of $\int_C\nabla(\vec r\cdot\vec a)\cdot d\vec r$? (Be sure you can explain why your answer is correct.)
maximum value of $\int_C\nabla(\vec r\cdot\vec a)\cdot d\vec r =$