Lemmara logoLemmaraWorked solution

0606/11 May/Jun 2025, Question 1: Unit Vectors and i, j Components

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use given column vectors and a vector equation in i and j to find a vector and two unknown scalars.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Given PQ = (−3, 7) and 4PR = (−2, 8), find the column vector RQ.

  1. 1PR = (1/4) × column vector (−2, 8) = column vector (−0.5, 2)
  2. 2RQ = RP + PQ = −PR + PQ
  3. 3RQ = column vector (0.5, −2) + column vector (−3, 7) = column vector (−2.5, 5)

AnswerRQ = column vector (−2.5, 5)

Part (b) · 3 marks

With a = αi + 6j, b = 4i + βj, c = (2α + 5β)i + 20j and c = 3a − 2b, find α and β.

  1. 13a − 2b = (3α − 8)i + (18 − 2β)j
  2. 2i: 3α − 8 = 2α + 5β
  3. 3j: 18 − 2β = 20, so β = −1
  4. 4Substitute β = −1: 3α − 8 = 2α − 5, so α = 3

Answerα = 3, β = −1

Stuck on a step? Read the free lesson: Unit Vectors and i, j Components

Practise more unit vectors and i, j components questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on unit vectors and i, j components

Also searched as: 0606/11/M/J/25 · 0606_s25_qp_11 · 0606 s25 11 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.