H2MA Remedial Vectors I, II (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Vectors I, II Basic Mastery Questions 1. ACJC Promo 9758/2021/Q10(i) Referred to the origin O, the points A, B and C have position vectors 42ij− , 2 −+i j k and 7 − − +i j k respectively, where  and  are constants. Given that A, B and C are collinear, show that  =5, and find the value of  . [3] Answer: 10 =− 2. JPJC Prelim 9758/2021/01/Q2 Referred to the origin O, the points A and B have position vectors a and b such that =++a i j k and 22= + +b i j k . (i) Find the size of angle OAB. [2] The point C has position vector c given by =+c a b , 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] Answer: (i) 144.7 (ii) 2= (iii) 32 52 52 c   =  3. RI Prelim 9758/2021/02/Q4(a)(i) Referred to the origin O, points A, B and C have position vectors a, b and c respectively. The three points lie on a circle with centre O and diameter AB (see diagram). Using a suitable scalar product, show that the angle ACB is 90 . [4] O A B C

Teacher’s copy 2 Standard Questions 1. MI Promo 9758/2021/PU2/02/Q4 Referred to the origin O, the points A and B are such that OA= a and OB = b . The mid-point of OA is P and the point M on PB is such that : 2 : 3PM MB = . By finding OM , show that the area of triangle OMP can be written as k ab where k is a constant to be found. [5] Given that 2, 2==ab and the angle AOB is radians4  , show that PM is perpendicular to OA. [4] Answer: 1 10k = 2. MI Promo 9758/2020/PU2/P1/Q7 In the parallelogram OABC, aOA= and cOC= . The point M on OA is such that OM : MA = 2 : 1 and the point N on AB is such that AN : NB = 1 : 2. It is given that the lines CM and ON intersect at point R. (i) Find OM and ON , giving your answers in terms of a and c . [2] (ii) Show that 62 11 11OR=+ ac . [4] (iii) Hence find the ratio CR : RM . [1] (iv) State, with a reason, whether the points O, B and R are collinear. [2] Answer: (i) 2 3OM = a , 1 3ON =+ac (iii) 9 : 2