You cannot do this with Stoke's theorem. Because Stoke's theorem is computing surface integrals,
you are asking a question about computing line integrals.
The question states: F(x,y,z)=(y-z, 7z-8, x-7y). Compute line integral F.ds along the unit circle c(t)=(cos(t), sin(t), 0), 0<=t<=2pi.
So by doing the line integral F(c(t)).c'(t) you get -2pi. But how do you go about it using Stokes Theorem? What is the parametrization and what form of it would you use? Curl of F.dS?
You cannot do this with Stoke's theorem. Because Stoke's theorem is computing surface integrals,
you are asking a question about computing line integrals.