While mapping a straight countryside road, a cyclist starts from village P taken as the origin and travels in three stages along the same road:
Stage-1: 12km west to point Q.
Stage-2: xkm east to point R.
Stage-3: 5km west to point S.
At the end of Stage-3 the cyclist is 8km west of village P.
(a) Taking west as the negative direction, write an equation connecting x with the given data and solve for x.
(b) Using the value of x obtained, calculate the total distance travelled by the cyclist.
(c) Find the magnitude of the net displacement of the cyclist from P to S and state its direction.