H2MA Remedial _ Vectors III (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Vectors III Basic Mastery Questions 1. ACJC Promo 9758/2020/Q8(i), (ii) The lines l and m are defined by the equations : (2 6 3 ), 13:. 44 l x a y zm a = − + − + − − +== r i k i j k (i) Given that the lines intersect, show that 6a= . [2] (ii) Find the position vector of N, the foot of perpendicular from the point (5, 0,1)A to the line l. [3] Answers: (ii) 11 1 127 1 ON  =− − 2. SAJC Promo 9758/2020/Q10 Relative to an origin O, the points A and C have position vectors 32+ik and 4 +ij respectively. The point C is such that OABC is a parallelogram and the point E divides AB in the ratio 1:3. The point M is the midpoint of CA. (i) Find the cartesian equation of line CA and the vector equation of line OE. [5] (ii) Find the position vector of point F, the point of intersection of CA and OE. Hence deduce the ratio :OF OE . [3] (iii) Find angle OMC, giving your answer correct to the nearest 0.1o. [3] (iv) Find the exact length of projection of OM onto CA. [2] Answers: (i) 16 1, 8   =  r (ii) 16 1 15 8 OF  =  , : 4 : 5OF OE = (iii) 102.8OMC= (iv) 1 6 units3

Teacher’s copy 2 Standard Questions 1. ACJC Promo 9758/2021/Q6 The Cartesian equation of line 1L is 2 2 3x y z a b c − + −== , where ,,abc are constants. The line 2L is parallel to the vector 43ij+ . The line 3L passes through the origin and the point with position vector jk+ . (i) Given that 1L is perpendicular to 2L , form an equation relating and .ab [1] (ii) Given that 1L intersects 3L , show that 5 2 2 0.a b c+ − = [3] (iii) Hence express and in terms of .a b c [1] Find the acute angle between 1L and 3L . [2] Answers: (i) 4 3 0ab+= (iii) 68 ;77a c b c= =− (iv) 86.7o 2. CJC Promo 9758/2021/Q9 With reference to the origin O, the points A and B have position vectors 2a i j k=− + + and 25b j k=+ respectively. (i) Find a vector equation of the line l1 that passes through point A and is parallel to the vector a. (ii) Find the exact length of projection of b on l1. Hence find d, the exact perpendicular distance from the point B to l1. [4] (iii) Using the value of d found in part (ii), find the position vector of the point C, the foot of perpendicular from the point B to l1. [3] (iv) The line l2 passes through point B and is parallel to vector b. Find a cartesian equation of l3 which is the reflection of l2 in l1.