Lemmara logoLemmaraWorked solution

0606/13 Oct/Nov 2025, Question 7: Unit Vectors and i, j Components

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using vectors with O at the origin, find OR parallel to −i + 5j with given magnitude, then find OP parallel to 2i − 3j given OQ.

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

Part (a) · 3 marks

Find the vector OR that points the same way as −i + 5j and has magnitude 3√26.

  1. 1OR = k(−i + 5j)
  2. 2|−i + 5j| = √(1² + 5²) = √26
  3. 3k√26 = 3√26, so k = 3
  4. 4OR = −3i + 15j

AnswerOR = −3i + 15j

Part (b) · 4 marks

Given OQ = 10i + 6j and OP parallel to 2i − 3j, find OP using the condition PQ is parallel to −i + 5j.

  1. 1OP = a(2i − 3j) and PQ = b(−i + 5j)
  2. 2OP + PQ = OQ: a(2i − 3j) + b(−i + 5j) = 10i + 6j
  3. 32a − b = 10 and −3a + 5b = 6
  4. 4Solving: a = 8, b = 6
  5. 5OP = 8(2i − 3j) = 16i − 24j

AnswerOP = 16i − 24j

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: 0606/13/O/N/25 · 0606_w25_qp_13 · 0606 w25 13 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.