Given the surface:
x^2 + y^2 + z^2 = 1 but x + y + z > 1 (actually greater than/equal to)
I'd like to parametrize both this portion of the sphere and I'd like to find a parameterization of the boundary of the surface (that is, the intersection of the above sphere and plane).
The Attempt at a Solution
Parametrizing the surface is killing me. If the portion of the sphere were rotated so that it was pointing towards the z-axis it would be parametrized simply by polar coordinates with theta going from 0 to 2Pi and Phi going from 0 to arcsin(3^(-1/2)), but for my problem I need to compute a certain flux (i would need to transform everything, which isn't even taught in this course). The surface isn't a function of any of the coordinate axes, and spherical parameters are useless.
The curve is also lost to me, I'm not sure how to satisfy both x^2 + y^2 + z^2 =1 and x + y + z = 1 with equations involving just one parameter.