RI Vectors C2A Add Prac (Qn)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 ______________________________ Additional Practice C2AVectors I Page 1 of 6 Additional Practice Questions for Chapter 2A: Vectors I Vector Algebra, Ratio Theorem, Scalar and Vector Products 1 Referred to an origin O, points A and B have position vectors given respectively by and22 236 .OA OB    ij k ij k    The point P on AB is such that :: 1 .AP PB  Show that ( 1 ) ( 25 ) ( 28 ) .OP      ij k  (i) Find the value of  for which OP is perpendicular to AB. (ii) Find the value of  for which angles AOP and POB are equal. [(i) 5 18 (ii) 3 10 ] 2 Referring to an origin O, the position vectors of points A, B and C are given by 7OA i  , 4OB ik   and 4OC ij   respectively. A parallelepiped has OA, OB, OC as three edges, and the remaining vertices are X, Y, Z and D as shown in the diagram. (i) Write down the position vector of Z in terms of i, j and k. [1] (ii) The point P divides CZ such that CP PZ  . Given that OP  is perpendicular to CZ  , find the value of  and evaluate OP  . [6] [(i) 84ik (ii) 4 ] A O B Z Y D X C

Raffles Institution H2 Mathematics 2025 Year 5 _____________________________________________________________________________________________ ___________________________ Additional Practice C2AVectors I Page 2 of 6 3 The position vectors of A and B with respect to the origin O are a and b respectively. M is the mid-point of OA and C is the point on MB such that 2CB MC      . Given that 6a , 5b and the angle between a and b is 45 , evaluate the exact value of the scalar product of b and c . [   5 53 23 ] 4 Referred to the origin O, the points A and B have position vectors a and b such that aij k and 22 bi j k . (i) Find the size of angle OAB. [2] The point C has position vector c given by  cab , where λ and µ are positive constants. Given that the area of triangle OAC is twice that of triangle OBC, (ii) find µ in terms of , [3] (iii) hence, if OC = 118, find the position vector c. [4] [(i) 144.7 (ii) 2  (iii) 32 52 52     ] 5 With respect to the origin O, the position vectors of the points A, B and C are a , b and c respectively. Point C lies on AB such that :1 : 2AC CB  . It is given that a is a unit vector and the length of OB is 2 units. (i) Give a geometrical interpretation of ac . [1] (ii) It is given that the angle AOB is 60 . By considering    22 ab ab , find 2 ab . [3] (iii) Find c in terms of a and b. [1] (iv) Hence by considering cosine of angle AOC and cosine of angle COB, determine if the line segment OC bisects the angle AOB. [3] [(ii) 2 (iii) 2 3 ba ]

Raffles Institution H2 Mathematics 2025 Year 5 __________