H2MA Remedial _ Vectors IV (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Vectors IV Basic Mastery Questions 1. RVHS CT 9758/2021/Q7 The plane  passes through the points with coordinates ( 1, 0, 1),− (2, 1, 1)− and (1, 3, 2)− . The line l passes through the point P (16, 20, 16) and is parallel to the vector 1 2 1    . (i) Find the cartesian equation of  . [3] RVHS JC Skills Builder: Click here or scan this to view video example on how to find vector equation of a plane! Also, click here or scan this to view video example on how to convert vector equation of a plane to Cartesian form! (ii) Find the coordinates of the point of intersection of l and  . [2] (iii) Find the acute angle between l and  . [2] RVHS JC Skills Builder: Click here or scan this to view video example on how to find vector equation of a plane! (iv) Determine a vector equation of the line of reflection of l in  . [4] RVHS JC Skills Builder: Click here or scan this to view video example! Answers: (i) 5 7 11 6x y z+ + = (ii) 3 6 3( , , )− (iii)  = 61.3 (iv) 37 62 3 31         = − +           r , R

Teacher’s copy 2 2. ACJC Promo 9758/2020/Q9 The plane  passes through the point with position vector 3−ik and contains the line with equation (2 )= + + − +r i j i j k . (i) Show that the cartesian equation of the plane  is 2 3 5x y z+ − = . [2] (ii) Find the shortest distance from ( 5, 6, 5)P −− to the plane  . [2] The line L that passes through P and is parallel to 3 2 2−+i j k intersects the plane  at the point Q. (iii) Find the coordinates of Q. [2] (iv) Hence or otherwise, find the length of projection of PQ on the plane  . [2] Answers: (ii) 8 14 (iii) Q(7, -2, 3) (iv) 1174 16.4 (3 s.f.)7 =

Teacher’s copy 3 Standard Questions 1. NJC CT 9758/2021/Q12 Diagram I: Louvre Museum Diagram II Diagram I shows the structural design of the Louvre Museum which is constructed entirely with glass segments and metal poles. As shown in Diagram II, the structure can be modelled by a right pyramid consisting of a square base PQRS of sides 30 metres on horizontal ground and the apex T. O is the centre of the square base and T is vertically above O with a perpendicular height of 20 metre