for the second problem i think i figured out how to get the radius. The vector equation is saying that the two vectors (r - a) and (r - b) are perpendicular to each other. If a right triangle is in a sphere, then the hypotnuse is the diameter of the sphere. So i got the magnitude of (r - a) and (r - b), then used pythagorean theorem to get the diameter, just divide by 2 and you have the radius. No clue how to get the center though. (sorry for poor spelling, been up for over 36 hours now)