RI T2W10+Vectors+1+%28Qn%29

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _____________________________________ Y6 H2 Math T2W10 Math Focus: Vectors 1 Page 1 of 1 Term 2 Week 10 Math Focus Topic: Vectors 1 1 The vectors u and v are given by u = 2i – j + 2k and v = ai + bk, where a and b are constants. (i) Find (u + v) × (u – v) in terms of a and b. [2] (ii) Given that the i- and k-components of the answer to part (i) are equal, express (u + v) × (u – v) in terms of a only. Hence find, in an exact form, the possible values of a for which (u + v) × (u – v) is a unit vector. [4] (iii) Given instead that (u + v).(u – v) = 0, find the numerical value of |v|. [2] 2 Vectors a, b and c are such that a  0 and 3 2 .a b = a c (i) Show that 3 2 , −=b c a where  is a constant. [2] (ii) It is now given that a and c are unit vectors, that the modulus of b is 4 and that the angle between b and c is 60 . Using a suitable scalar product, find exactly the two possible values of . [5] 3 With reference to the origin O. the points A, B, C and D are such that OA= a , OB= b , 24OC=+ ab and 5OD=+ba . The lines BD and AC cross at X (see diagram). (i) Express OX in terms of a and b. [4] The point Y lies on CD and is such that the points O. X and Y are collinear. (ii) Express OY in terms of a and b and find the ratio OX : OY. [6]