Please help on these problems

10. In the figure OABC is a trapezium in which 3 AB = 20C. S divides OC in the ratio 2:1 and AS produced meets BC produced at T Given that OC = 3c and OA = a (a) Express AS and BC in terms of a and c (b) Given further that AT = hAS and BT = KBC where h and k are constants (i) Express AT in two ways in terms a, c . h and k (c) The obtuse angle between the lines PQ (d) Hence find the ratio BT: BC 11. S R O In the figure above, OPQ is a triangle in which OS = 34 OP and PR: RQ = 2 : 1. Lines OR and SQ meet at T. (a) Given that OP = P and OQ = q, express the following vectors in term of p and q (i) PQ 0 (ii) OR (iii) SQ (b) You area further given that ST = m SQ and OT = n OR. Determine the values of m and n5. In the figure below, DE = 12 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 (1) BD (1mk) (ii) BC (1mk) (iii) CD (Imk) (iv) AC (2mks) b) Given that AC = KCE; where k is a scalar, Find (i) the value of k (4mks) (ii) the ratio in which C divide AE. (1mk) 6. In the figure alongside OA = a , OB = b. T lies on AN such that AN : TN = 13:6. M lies on AB such that AM:MB=1:3 and M N lies on OB such that OB: BN = 7:-5.~ B (@) Express in terms of a and b in the simplest form (1) AN N Bii) AT (iii) AM (b) Show that O, T and M are collinear and state the ratio of OT: TM 7. A point (-3, 4) divides AB internally in the ratio 3:5. Find the coordinates of point A given that point B is (6, -5) 8. Given that O is the origin, OA = 3i + 2j - 4k and OB = 6i + 11j + 2k. If x divides AB in the ratiol:2, find the modulus of OX to 2d.p 9. a) Expand (2 - '/5x)5 b) Hence use the expansion to find the value of (1.96) correct to 3 decimal places