I am having some trouble finding the curve, C, of intersection of the plane x+y+z=1 and the sphere x^2+y^2+z^2=1. I then have to find the center of the curve C and the radius of the circle as well as find two perpendicular unit vectors parallel to the plane of C? They even give me one of those vectors and ask for me to use that to find the other, v1= (i-j)/sqrt(2). Then I have to use these results to construct a parametrization of C.
Any help with this is appreciated.