Lemmara logoLemmaraWorked solution

0606/12 Feb/Mar 2026, Question 9: Unit Vectors and i, j Components

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using vectors for two moving particles and a point on a line, find positions, test for collision, and determine integer coordinates at a set distance.

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

Part (ai) · 1 mark

Give B's position vector as a function of t, starting from (−3, 4) with velocity (4, −2).

  1. 1Position = start + t × velocity
  2. 2r_B = (−3, 4) + t(4, −2) = (−3 + 4t, 4 − 2t)

Answercolumn vector (−3, 4) + t × column vector (4, −2), i.e. column vector (−3 + 4t, 4 − 2t)

Part (aii) · 4 marks

Decide whether A and B ever occupy the same point, showing your reasoning.

  1. 1Position of A: t(2, 1) = (2t, t)
  2. 2Collide if (2t, t) = (−3 + 4t, 4 − 2t) for the same t
  3. 3x: 2t = −3 + 4t gives t = 3/2
  4. 4y: t = 4 − 2t gives t = 4/3
  5. 5The values of t differ, so the particles do not collide

AnswerThe particles do not collide: equating components gives t = 3/2 and t = 4/3, which are inconsistent

Part (b) · 5 marks

With Q at 3i + 2j and R at −i + 4j, find integer a and b so S = ai + bj lies on line QR and RS has length √5.

  1. 1QR = (−i + 4j) − (3i + 2j) = −4i + 2j
  2. 2|QR| = √(16 + 4) = 2√5, so |RS| is half of |QR|
  3. 3RS = ±(1/2)QR = ±(−2i + j)
  4. 4OS = OR + RS: (−1 − 2)i + (4 + 1)j = −3i + 5j, or (−1 + 2)i + (4 − 1)j = i + 3j
  5. 5a = 1, b = 3 or a = −3, b = 5

Answera = 1, b = 3 or a = −3, b = 5

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: 0606/12/F/M/26 · 0606_m26_qp_12 · 0606 m26 12 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.