1. The problem statement, all variables and given/known data Sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function using the given parameter. 2. Relevant equations z = x^2 + y^2, x + y = 0, x = t 3. The attempt at a solution Space curve sketched (elliptic paraboloid corresponding to z-axis) Vector valued function: x = t, y = -t; z = t^2 + (-t)2; z = 2t^2; r(t) = ti - tj + 2t^2k **Intersection of the surface, not sure how to obtain this. I have the feeling once I get it I'm gonna be shaking my head for having forgotten something. So I've tried setting x^2 + y^2 = x + y tried substituting in t for x and y values tried reverse engineering what I'm supposed to do with the answers plugged in to the equations. tried finding x int, y int, and z int. Just don't know how to procede. Any assistance is greatly appreciated.