Only some hints:

1. The curve of intersection between a sphere and a plane is a circle.

2. The normal vector of the plane p is

3. The midpoint of the sphere is M(0, 0, 0) and the radius is r = 1.

4. A straight line through M perpendicular to p intersects p in the center C of the circle. You should come out with . So the distance of C to M is

5. Use r and d to determine the radius of the circle.

6. A vector parallel to p is perpendicular to , that means

I'll show you how to get in general:

7. For the parametrization of the curve C you have to use the sine and cosine function.