S.4 Mathemetics Vectors Caltec S.4

VECTOR EXERCISE PART TWO 1. In a triangle OAB, , a OA b, OB P and Q are points on OA and AB respectively such that 3OP = PA, AQ = 2QB and N is the midpo int of OQ. ANM is a straight line which is such that AN = 5NM. Given also that OB, OM h  where h is a scalar. (a) Expr ess the following vectors in terms o f a and b: (i) OQ (ii) AN (iii) PN (iv) NB (b) Show that the points P, N and B are collinear (c) Find t he value of h. 2. In the figure below, P is a point on AD such that PD : AP = 1 : 2, , a OA b, OB 3OB = 2BD and OC = 3CE = 3AP. (a) Expr ess the following vectors in terms o f a and b: (i) AD (ii) BP (iii) DC (b) Show that AD : OE = 3 : 8 3. In the figure below, , 3 a PT b, 3 PR ,PT PQ 4  PV 2PS  and .RT 3RS 2  (a) Expr ess the following vectors in terms o f a and b: (i) RS (ii) PV (iii) RQ (b) Find t he ratio of RV to RQ. 4. In the figure below, , a OA b, OB F and G are points on AC such that AF : AB = 3 : 4 and AG : AC = 2 : 3. Point D is on OA such that OD : DA = FB : BG = 1 : 2.    a b A O D C E P B P T Q R V S 3a 3b (a) Expr ess AG and AC in terms o f …