Lemmara logoLemmaraWorked solution

0580/22 Feb/Mar 2022, Question 22: Expressing Vectors in Terms of a and b

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Trapezium OPQR with O at origin, OR = a, OP = b, and RQ parallel to OP with length 3/5 of OP. Find vector PQ, then locate intersection W of extended PQ and OR.

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

Part (a) · 2 marks

Express the vector from P to Q using a and b, simplified.

  1. 1→RQ = (3/5)b
  2. 2→PQ = −b + a + (3/5)b
  3. 3→PQ = a − (2/5)b

Answera − (2/5)b

Part (b) · 2 marks

Lines PQ and OR are extended to meet at W; determine W's position vector.

  1. 1W lies on OR extended, so →OW = ka
  2. 2Triangles WRQ and WOP are similar, with RQ : OP = 3 : 5
  3. 3So WR : WO = 3 : 5, giving OR : OW = 2 : 5
  4. 4→OW = (5/2)a

Answer(5/2)a

Stuck on a step? Read the free lesson: Expressing Vectors in Terms of a and b

Practise more expressing vectors in terms of a and b questions

Real 0580 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 expressing vectors in terms of a and b

Also searched as: 0580/22/F/M/22 · 0580_m22_qp_22 · 0580 m22 22 · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.