show your work

3. In the figure below OA = a , OB = band DB is parallel to OA. C is on AB extended such that AB: BC = 2:1 and that OA = 3DB. a) Express the vector BC in terms of a and b. (1mk) b) Show by vector methods that the points O, D and C are collinear. (3mks) 4. In the figure below OP = - a+b. OR = _a-b. RQ = $kb+ - ma, where k and m are scalars 2PS = 3SR. (a) Express as simply as possible in terms of a and beach of the following vectors. (i) PR (1mk) (ii) PS (1mk) (iii) os (1mk) (b) Express OQ in terms of a, b, k and m. (2mks) (c) If Q lies on OS produced with OQ: OS= 5:4, find the value of k and m. (5mks) 5. In the figure below, DE = 1/2 AB and BC = 2/3 BD and the co ordinates of A.B and D are (5,4),(9,6) and ( 12,0) respectively. B(9,6) C A(5,4) D(12,0) Find the vectors (i) BD (1mk) (ii) BC (1mk) (iii) CD (1mk) (iv) AC (2mks) b) Given that AC = KCE; where k is a scalar, Find (1) the value of k (4mks) (ii) the ratio in which C divide AE. (1mk)