Prime DSE Series - Mathematics Mock Exam Papers (Extended Part) Module 2 Set 3

HKDSE-MATH-EP(M2)(Set 3) − 22 22 © United Prime Educational Publishing (HK) Ltd. Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. 11. Let O be the origin. The coordinates of A , B and C are (0, − 1, 5) , (2, 0, 2) and (2, − 1, 1) respectively. Let D be a point lying on the straight line passing through B and C such that AD is perpendicular to BC . Denote the circle passing through A , C and D by Γ . (a) By considering CD  as a scalar multiple of CB  , find OD  . (4 marks) (b) Let G be the circumcentre of Γ . Find the coordinates of G . (2 marks) (c) Let Π be the plane which contains Γ . Denote the projection of point P ( − 4, − 1, 1) on Π by Q . (i) Find the coordinates of Q . (ii) Someone claims that Q lies on Γ . Do you agree? Explain your answer. (6 marks) Sample © United Prime Educational Publishing (HK) Limited All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publisher.