Let $\mbox{curl }\vec F = -3y\,\mathit{\vec i}-3z\,\mathit{\vec j}+\,\mathit{\vec k}$, let $P =(5,3,2)$, and let $C$ be the circle of radius 0.02 centered at $P$ in the plane $x+y+z = 10$, oriented clockwise when viewed from the origin.

(a) Find $\mbox{curl }\vec F\cdot(\vec i+\vec j+\vec k)$ at $P$.
$\mbox{curl }\vec F\cdot(\vec i+\vec j+\vec k) =$

(b) Use your answer to part (a) to estimate $\int_C \vec F\cdot d\vec r$.
$\int_C \vec F\cdot d\vec r \approx$