SPM 2019 Add Maths Paper 2, Question 6Vectors

Solution by scale drawing is not accepted. Diagram 3 shows the positions of jetty O and kelongs K, L, R, S and T in the sea. Kelong L is situated 400 m from jetty O and kelong R is situated 600 m from jetty O in the direction of OL. Kelong S is situated 300 m from jetty O and kelong T is situated 600 m from kelong S in the direction of OS. Kelongs L, K and T are situated on a straight line such that the distance of kelong K from kelong T is 5 times its distance from kelong L. (a) By using p to represent 100 m in the direction of OR and q to represent 150 m in the direction of OT, express in terms of p and q (i) vector OK, (ii) vector RK. (b) If Joe uses a binocular to observe kelong R from kelong S, determine whether kelong R can be seen without being blocked by kelong K or otherwise. Prove your answer mathematically.