parameterization and path integral

Hey all, I have a question here and I can't seem to get around solving it.

Show that the circle that is the intersection of the plane x + y + z = 0 and the sphere x^2 + y^2 + z^2 = 1 can be expressed as

x(t) = (cos t - sqrt(3)sin t)/sqrt(6)

y(t) = (cos t + sqrt(3)sin t)/sqrt(6)

z(t) = - 2cos t/sqrt(6)

where 0<t<2π

And then, the question continues to...

Calculate the path integral where f(x,y,z)=xy-z and c is a path on the circle in the first part starting from the point (-1/sqrt(2),1/sqrt(2), 0) and finishing at the point (1/sqrt(2),-1/sqrt(2), 0), in the direction of increasing t.

Some help please?