SPM 2024 Add Maths Paper 2, Question 4Vectors

Solved on video in English and Bahasa Melayu · Form 4, Vectors · 6:23 video

The question

Diagram 2 shows triangle ABC. AR is parallel to PQ.

It is given that CB = 6u, CA = 5v and AR = (2/5)AB.

(a) Express in terms of u and v: (i) AB (ii) CR

(b) (i) Given that u = 5i and v = i + 4j, find |CR|. (ii) Hence, find the shortest distance from point A to the straight line CR if the area of △CPQ is 40/3 unit² and CQ:QR = 1:2.

Step 1

Using triangle law on △ABC:

13 more steps, each with the reason for it, in the full solution

Final answer

AB = 6u − 5v; CR = (12/5)u + 3v; |CR| = 3√41 ≈ 19.21 units; distance = 80√41/41 ≈ 12.49 units

Where students lose marks

Watch out: area scales by k², not k. △CAR is the bigger triangle, so multiply 40/3 by 3² = 9, not by 3.

Watch every step of this question solved on video (6:23), with the reason behind each step and a box that checks your own answer.

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