SPM 2018 Add Maths Paper 2, Question 8Vectors
Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Vectors · 9:22 video
The question
Diagram 5 shows triangles OAQ and OPB where point P lies on OA and point Q lies on OB. The straight lines AQ and PB intersect at point R. It is given that OA = 18x, OB = 16y, OP:PA = 1:2, OQ:QB = 3:1, PR = m·PB and QR = n·QA, where m and n are constants. (a) Express OR in terms of (i) m, x and y, (ii) n, x and y. (b) Hence, find the value of m and of n. (c) Given |x| = 2 units, |y| = 1 unit and OA is perpendicular to OB, calculate |PR|.
[10 marks]
9:22Step 1
Since OP:PA = 1:2, OP = (1/3)OA = (1/3)(18x) = 6x.
Why this step
The whole line is 1 + 2 = 3 parts and OP takes 1, so OP = 1/3 of OA, not 1/2. Do the same for OQ:QB.
11 more steps, each with the reason for it, in the full solution
Final answer
(a)(i) OR = (6 − 6m)x + 16my; (a)(ii) OR = 18nx + (12 − 12n)y; (b) m = 2/3, n = 1/9; (c) |PR| = 40/3 units ≈ 13.33 units
Where students lose marks
Watch out: PB = OB − OP, not OP − OB. In (c), the cross term vanishes only because OA ⊥ OB.
Watch every step of this question solved on video (9:22), with the reason behind each step and a box that checks your own answer.
No card. Every past-year question on video, in English and BM.
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