a. The four points O, A, B and C are such that OA(vectors) = 5a, OB(vectors) = 15b, OC(vectors) = 24b = 3a. Show that B lies on the line AC.

b. Relative to an origin O, the position vector of the points P is I – 4j and the position vectors of the point Q is 3i + 7j. Find

i. |PQ(vectors)|.

ii. The unit vector in the direction PQ(vectors).

iii. The position vector of M, the mid-point of PQ.