When a particle moves in a circle with constant speed, the magnitudes of its position vector and velocity vector are constant. 

(a) Differentiate r·r = r² = constant with respect to time to show that v·r = 0 and therefore v_┴r. 

(b) Differentiate v·v = v² = constant with respect to time and show that a·v = 0 and therefore a_┴v. What do the results of (a) and (b) imply about the direction of a? 

(c) Differentiate v·r = 0 with respect to time and show that a·r + v² = 0 and therefore ar = -v²/r.