1. Consider the sphere in R3 x2 + y + 2 = 1. In this question, we will outline the procedure for computing the Gauss curvature of the sphere. The Gauss curvature is a notion of curvature for surfaces. (d) Write the equation for the plane passing through P containing the unit normal computed in (a) and the vector v. Sketch this plane and the sphere (you can take say a = 0 for the sketch). (e) Sketch the curve of intersection of the plane computed in (d) and the sphere. Write down a parametric equation r(t) for this curve. (f) Compute the curvature of the curve r(t) at P. (The product of the maximum and minimum curvatures obtain in this way is called the Gauss curvature of the surface.) The unit normal found in subpart a is: POINT P = (0,0,1) Vector v = (cos(alpha), sin(alpha),0) where 0 POINT P = (0,0,1) Vector v = (cos(alpha), sin(alpha),0) where 0