TMJC Term 4 Revision Chapter 5 & 6 Vectors and 3D Vector Geometry Questions

Term 4 Revision Topical Quick Check: Vectors & 3D Vector Geometry TMJC 2024 JC1 H2 Mathematics (9758) Term 4 Revision Topical Quick Check Chapter 5 Vectors Chapter 6 3D Vector Geometry 1 CJC Promo 9758/2022/Q9 Relative to the origin O, the position vectors of points A, B and C are a, b and c respectively, where b is a unit vector. It is given that b and b − a are perpendicular and C lies on AB such that : 3:1AC CB = . (i) Show that sec=a , where  is the angle between a and b. [3] By expressing c in terms of a and b, (ii) find the value of cb and state the geometrical interpretation of cb , [4] (iii) find the value of   bc ab . [2] 2 ACJC Promo 9758/2022/Q5 The line L has vector equation 62 : 0 1 11 L  −       =+       −    r ,  . (i) Find the position vector of the point N, the foot of perpendicular from the point A with coordinates (3, 6,1) to the line L. [3] (ii) Find the position vector of the point 'A , the reflection of point A in the line L. [2] (iii) Find the coordinates of the points on the line L that are 33 units away from point A. [2]

Term 4 Revision Topical Quick Check: Vectors & 3D Vector Geometry TMJC 2024 3 JPJC Promo 9758/2022/Q13 The planes 1P and 2P have equations 4 3 1 1 1 3 3 7 12 r st            = − + − + −                and 31xy+= respectively, where s and t are parameters. (i) Find the line of intersection of 1P and 2P . [3] (ii) Find the acute angle between 1P and 2P . [2] The point A has position vector 5 4 15i j k−+ and the point B has position vector 2−i k. (iii) Find the foot of perpendicular from A to 2P . [3] (iv) Find the length of projection of AB onto 2P . [3] 4 TMJC Promo 9758/2022/Q10 Fig. 1 shows a rectangular prism. Fig. 2 shows the prism with a removed part that was cut along the plane .ABFE The resulting object has a base ,ABCD a top ,EFGH a side ,CDHG and a slanted side .ABFE The following information is given. The top EFGH is a part of the plane with equation 4 6.x y z+ − =− The base ABCD is a part of the plane with equation 4 7.x y z+ − = The slanted side ABFE is a part of the plane with equation 3 4 9 15.x y z+ + = (i) Find the acute angle between the base and the slanted side. [2] (ii) Find the height of the object, measured in the direction perpendicular to the base. [3] (iii) Find a vector equation of the line of intersection between the base and the slanted side. [2] A B C D E F G H Fig. 2 A B C D G H Fig. 1

Term 4 Revision Topical Quick Check: Vectors & 3D Vector Geometry TMJC 2024 Point S with coordinates ( )2,11,12 lies on .CD (iv) Find the position vector of the foot of the perpendicular from point S to the line found in part (iii). [3] (v) A part of the object is to be further removed so that the remaining object is now symmetric