SPM 2021 Add Maths Paper 1, Question 7Vectors

Solved on video in English and Bahasa Melayu · Form 4, Vectors · 5:05 video

The question

(a)

Diagram 4 shows the locations of four stations in a school field on a Cartesian plane such that BCDE is a parallelogram, with B(5, 11) and E(1, 1). State the value of |ED + DB + BE| (the magnitude of the resultant vector ED + DB + BE).

(b)

A path from station E to station D is parallel to the x-axis and the displacement is 11 m. Using the vector triangle law, find the resultant vector from station E to station C. (BCDE is a parallelogram with B(5, 11) and E(1, 1).)

(c)

A boy runs from station E to a cone at K(5, p) with a constant velocity of (3i + 4j) m s⁻¹. He takes t seconds to reach the cone. Based on the given information, write a vector equation in terms of t and p. Hence, find the value of t and of p. (E is at (1, 1).)

SPM 2021 Add Maths Paper 1, Question 7: the question as drawn in Eduly's video5:05

Part (a)

Step 1

Add the vectors head-to-tail: ED + DB = EB (going E → D → B).

Why this step

Vectors placed head-to-tail combine into one: E → D → B ends where E → B ends. That is the triangle law.

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

Final answer

0 unit

Where students lose marks

Watch out: ED + DB + BE is a closed path, so it is the zero vector, not |OE| = √2.

Part (b)

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

Final answer

EC = 15i + 10j

Where students lose marks

Watch out: write vectors with unit vectors i and j, never x and y (not 15x + 10y).

Part (c)

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

Final answer

4i + (p − 1)j = t(3i + 4j); t = 4/3, p = 19/3

Where students lose marks

Watch out: use the displacement EK, not the position vector OK, when linking displacement, velocity and time.

Watch every step of this question solved on video (5:05), with the reason behind each step and a box that checks your own answer.

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