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)
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?