RI Vectors C2B Add Prac (Qn)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 _____________________________________________ Additional Practice Questions for Chapter 2B: Vectors II Page 1 of 4 Additional Practice Quest ions for Chapter 2B: Vectors II – Equation of Straight Lines 1 Referred to the origin O, the position vector of the point A is 226ij k and the cartesian equation of the line l is 12 6x yz  . Find (i) the position vector of the foot of the perpendicular from A to l, [3] (ii) the perpendicular distance from A to l, [2] 2 The line 1l has equation 12 12 , 3      r where  is a parameter. (i) Find the exact shortest distance between the origin O and 1.l [3] Another line 2l has equation 13 .229 x yz  (ii) Write down a vector equation of 2.l [1] (iii) Show that 1l and 2l are skew lines. [3] (iv) Find a vector that is perpendicular to both 1l and 2.l [1] The points P and Q lie on 1l and 2l respectively, such that the line PQ is perpendicular to both 1l and 2.l (v) Find a vector equation of the line PQ. [3] 3 The line 1l has equation 55 3 x z m   , 2y  and the line 2l has equation 5 x y , 0z  , where m is a constant. It is given that 1l and 2l intersect at point A. (i) Find the value of m, and the coordinates of A. [4] (ii) Find the position vector of the point P on 1l such that OP is perpendicular to 1l , where O is the origin. [3] (iii) Find a vector equation of the line which is a reflection of 2l in 1l . [3]

Raffles Institution H2 Mathematics 2025 Year 5 ____________________________________ _____ ______________________________________________ Additional Practice Questions for Chapter 2B: Vectors II Page 2 of 4 4 The points A and B have position vectors 8 3 2     and 2 3 4     respectively. (i) Show that 22 6AB . [1] (ii) Find the cartesian equation for the line AB . [2] (iii) The line l has equation r 22 36 45 t        . Find the length of the projection of AB onto l . [2] (iv) Calculate the acute angle between AB and l , giving your answer correct to the nearest degree. [2] (v) Find the position vector of the foot N of the perpendicular from A to l . Hence find the position vector of the image of A in the line l . [4] 5 With reference to the origin O, the points A and B have position vectors 2ai j k   and 25bj k respectively. (i) Find a vector equation of the line l1 that passes through point A and is parallel to the vector a. [ 1 ] (ii) Find the exact length of projection of b on l1. Hence find d, the exact perpendicular di