NJC 1A Vectors Tutorial

National Junior College Mathematics Department 2025 – 2026 / H2 Maths / Vectors I / Tutorial Page 1 of 6 National Junior College 2025 – 2026 H2 Mathematics Topic 1A Vectors I Tutorial Check Your Understanding 1 The diagram below shows a rectangular cuboid OADBFCEG with dimensions OA = 6 units, OB = 2 units and OC = 3 units. (a) Find the following vectors, giving your answers in column vector notation. (i) ,OE ⎯⎯ → (ii) ,OG ⎯⎯ → (iii) ,CB ⎯⎯ → (iv) .CD ⎯⎯ → State another two displacement vectors that are equal to OE ⎯⎯ → and CB ⎯⎯ → respectively. (b) Find the magnitude of .CD ⎯⎯ → Hence, or otherwise, find two distinct vectors that are parallel to CD ⎯⎯ → and has length 21 units each. (c) The lines OG and CD intersect at point P. Find the position vector of P. (d) The point Q is such that E lies on the line segment BQ and BQ : EQ = 3 : 2. Find the position vector of Q.

National Junior College Mathematics Department 2025 – 2026 / H2 Maths / Vectors I / Tutorial Page 2 of 6 2 For each of the following pairs of vectors, find their scalar product. (a) 3+−i j k and 2,+ik (b) 1 4 3  − and 1 3 1 − − . 3 Relative to an origin O, the position vectors of the points A and B are 2−+i j k and 2−+ij respectively. Find (a) ,AOB (b) .OBA 4 Relative to an origin O, A and B have position vectors 2c+−i j k and 2c− + +i j k respectively, where c is a real constant. Find the value of c (a) if OA ⎯⎯ → is perpendicular to ,OB ⎯⎯ → (b) if instead 120 .AOB =  5 For each of the following pairs of vectors, find their vector product. (a) 3+−i j k and 2,+ik (b) 1 4 3  − and 1 3 1 − − , (c) 26−ik and 3 0 9 −   . 6 Relative to an origin O, the position vectors of the vertices A, B and C of a triangle are ,+−i j k 23++i j k and 54+−i j k respectively. (i) Find the exact area of triangle ABC. (ii) Find the length of projection of AB ⎯⎯ → onto .AC ⎯⎯ → (iii) Find the projection vector of AB ⎯⎯ → onto AC ⎯⎯ → in the form ( )1 5 abc++i j k for some integers a, b and c to be determined. (iv) Find the length of the vector component of AB ⎯⎯ → perpendicular to AC ⎯⎯ → in the form n for some integer n to be determined. (v) Find the vector component of AB ⎯⎯ → perpendicular to AC ⎯⎯ → in the form ( )1 5 p q r++i j k for some integers p, q and r to be determined.

National Junior College Mathematics Department 2025 – 2026 / H2 Maths / Vectors I / Tutorial Page 3 of 6 Practice Questions 1 (a) Relative to the origin O, the position vectors of two points A and B are t=+a i k and 2= − +b i j k respectively, where t . Given that the angle between a and b is 60 , evaluate the possible exact values of t. (b) Relative to the origin O, the position vectors of the points P and Q are p and q respectively. The point R lies on PQ produced such that :