I really do not know how to solve this one. I did a lot of research on the internet and could not find an answer.
Find the work done by moving a particle over $C$, where $C$ is the intersection of the upper hemisphere $x^2 + y^2 + z^2 = a^2$ with the cylinder $x^2 + y^2 = ax$ , $a>0$. Force field is $F = (y,z,x)$
My main problem is that I can't really picture $C$. Any help is appreciated. If it can be solved with Stoke's Theorem as well I would like to see that answer too.
The intersection is a tear shaped curve $C$.
Have a look at this interactive GeoGebra worksheet here: link
You might move around the circle of the cylinder with center at $(a/2, 0, 0)$ and radius $a/2$, and adjust the height according to the sphere: \begin{align} x(t) &= a/2 + (a/2) \cos t \\ y(t) &= (a/2) \sin t \\ z(t) &= \sqrt{a^2 - (x(t)^2 + y(t)^2)} \end{align}