1. The problem statement, all variables and given/known data I have a problem where I have a sphere with radius R centered at (0,0,0), and two given points on the surface of the sphere A=(a1,a2,a3) and B=(b1,b2,b3). I have to find/derive a parametric equation to describe the path from point A to point B along the surface of the sphere. 2. Relevant equations I need to provide x(t)=?, y(t)=?, z(t)=? in general terms to describe the path between any two points on the surface of a sphere with any radius. 3. The attempt at a solution When giving values to the points I can figure out how to find a plane that passes through the center of the sphere and the two points, but I don't know how to make a parametric equation to describe the circle of intersection between the sphere and the plane. If I could do that, I could set the parameters to only give me the portion of arc from A to B. I'm not exactly sure that I'm on the right track with the plane/sphere intersection idea, so any help would be much appreciated.