TMJC H2 Maths 9758 Chp 1 & 2 H2_MYE_Revision Package_Vectors

JC2 H2 MYE Revision Package: Vectors1 &2 TMJC 2020 Page 1 of 6 JC2 MYE Revision Package H2 Mathematics (9758) Vectors 1 2010Promo/RVHS/6 The position vectors of vertices A, B and C, relative to the origin O, are 34ik , 243  i j k and 11 4 9i j k respectively. (i) Find a unit vector parallel to OA . [1] (ii) A point P divides AC in the ratio 1 : 3. Find the position vector of P. [2] (iii) Show that the points O, B and P are collinear. [2] (iv) OBDC forms a parallelogram. Find the position vector of D. [2] 2 2015Promo/DHS/I/2 The position vectors of the points A and B relative to the origin O are 2 1 1   and 2 5 1   respectively. The point P lies between A and B such that AP AB where 01  . (i) Find the position vector of P in terms of . [1] (ii) If OP is perpendicular to AB , find the value of . [2] Given that 1 3  , (iii) Find the area of triangle OPA. [2] (iv) Write down the ratio of the area of triangle OPB to the area of triangle OPA. [1] 3 2013Promo/MJC/I/4 Referred to the origin O, the points A and B are such that OA a and , whereOB b a and b are non-zero and non-parallel vectors. The point C lies on OB such that ,OC kOB where k is a constant. P is on AC such that AP : PC = 3 : 1, and Q is on AB such that AQ : AB = 2 : 3. (i) Find OP and OQ in terms of a, b and k . [2] (ii) Given that O, P and Q are collinear, find the value of k . [3]

JC2 H2 MYE Revision Package: Vectors1 &2 TMJC 2020 Page 2 of 6 4 2015Promo/NYJC/1/4 Relative to the origin O, the position vectors of two points A and B are a and b respectively, where a and b are non-zero and non-parallel vectors. The vector a is a unit vector which is perpendicular to 25ab . The angle between a and b is 2 3  . (i) Show that 4 5b . [3] (ii) The point M divides AB in the ratio :1  . The point N is such that OMBN is a parallelogram. By considering ON in terms of a and b , find the area of triangle OAN in terms of  . [4] 5 RI Promo 9758/2017/2 Referred to the origin O, points A and B have position vectors a and b respectively, such that a and b are non-parallel vectors. Point C lies on line AB, such that the length of projection of OC onto OB is 5 units. Given that 2b and 1,ab find the possible position vectors of C in terms of a and b. [6] 6 2014 Promo/SAJC/5 (a) Relative to an origin O, the position vectors of A and B are a and b respectively, and c is the position vector of the point C on AB which divides AB in the ratio 3:1. Given that angle AOB is acute, show that the length d of the projection of OC on OB is given by 3. .44d  abb b [4] (b) Three vectors p, q and r are such that ,  p q p r p0 . Show that ,kq r p where .k [2] 7 2012/YJC/II/1 Two planes 1 and 2 have equations 22x y z   and 23x y z   respectively. The point A has coordinates (4, –1, 2). (i) F