RI Vectors C2B Add Prac (Soln)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 _____________________________________________ Additional Practice Questions for Chapter 2B: Vectors II Page 1 of 23 Additional Practice Quest ions for Chapter 2B: Vectors II – Equation of Straight Lines (Solutions) 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] TPJC Prelim 9740/2013/01/Q10 (modified) (i) 11 :2 1 , 61 l           r  Let B be the foot of perpendicular from A to l. 11 2 6 1 .1 0 1 4 11 533 17 OB AB AB OB                           (ii) 6Perpendicular distance from to 2 11s 3i1 1 3AlA B    

Raffles Institution H2 Mathematics 2025 Year 5 ____________________________________ _____ ______________________________________________ Additional Practice Questions for Chapter 2B: Vectors II Page 2 of 23 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] ASRJC Promo 9758/2021/Q8 (i) 1Shortest distance from to 12 12 03 449 3 3 4 449 34 17 2 units Ol                (ii) 2 2 13 1 3 0: 229 2 29 12 :3 2 , 09 xy z x y zl l                      r 

Raffles Institution H2 Mathematics 2025 Year 5 ____________________________________ _____ ______________________________________________ Additional Practice Questions for Chapter 2B: Vectors II Page 3 of 23 (iii) 1 2 12 :1 2 , 03 12 :3 2 , 09 l l                                 r r   Clearly, 2 2 3   and 2 2 9   are not scalar multiples of each other, hence both lines are not parallel. 12 12 12 32 03 09 1 2 1 2 --- (1) 1 2 3 2 --- (2) 3 9 --- (3)                       