Question 14 (15 marks) (a) Points A and B have position vectors OA = 21 + / and OB =-21+41. (i) Find the projection of AO onto AB. N (ii) Hence, or otherwise, find the perpendicular distance of AB from O. N (b) A cycloid is the path traced by a point on the circumference of a circle as it rolls along the x-axis. 5 re 2atr For a circle of radius r, it is described by the parametric equations x = r(0 - sin e) y= r(1 -cos 0 ) where 0 is the angle the radius to the particular point on the circumference makes with a vertical line. The arc length f can be calculated by evaluating dx de + dy do. Find the distance, in terms of r, a point on the circumference travels in one complete rotation