Selangor Trial 2025 Add Maths Paper 1, Question 7Vectors

Solved on video in English · Form 4, Vectors · 7:06 video

The question

(a)

It is given that u = b − a and v = c − b, with a = (3, 4), b = (5, 7) and c = (m, 3) (written as column vectors).

(a) Find u.

(b)(i)

It is given that u = b − a and v = c − b, with a = (3, 4), b = (5, 7) and c = (m, 3).

(b) If u is parallel to v, (i) find the value of m.

(b)(ii)

(b)(ii) Hence, find |u| : |v|.

Step 1

u = b − a = (5, 7) − (3, 4).

Why this step

Follow the order in the definition: b first, then take away a. Reverse it and you get (−2, −3), the exact slip examiners keep seeing.

1 more step, with the reason for it, in the full solution

Final answer

u = (2, 3) (column vector)

Where students lose marks

Watch out: u = b − a, so subtract a from b. Reversing it gives (−2, −3), which is wrong.

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

Final answer

m = 7/3

Where students lose marks

Watch out: parallel means u = λv, not u = v. Also check the second component of v: 3 − 7 = −4.

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

Final answer

|u| : |v| = 3 : 4

Where students lose marks

Watch out: substitute m = 7/3 into v first, and simplify √208 to 4√13 so the ratio reduces to 3 : 4.

Watch every step of this question solved on video (7:06), with the reason behind each step and a box that checks your own answer.

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