Lemmara logoLemmaraWorked solution

4PM1/01R Jan 2023, Question 4: Unit Vectors and i, j Components

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Vectors OA = πi + 2pj and OB = 5i + 9pj with AB parallel to i − 2j; find p, then AB, then a unit vector along OA in the specified form.

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

Part (a) · 6 marks

Use the condition that vector AB is parallel to i − 2j to determine the value of p.

  1. 1AB = OB − OA = (5i + 9pj) − (pi + 2pj) = (5 − p)i + 7pj
  2. 2Set (5 − p)i + 7pj = Q(i − 2j)
  3. 35 − p = Q and 7p = −2Q
  4. 47p = −2(5 − p) → 5p = −10
  5. 5p = −2

Answerp = −2

Part (b) · 2 marks

Substitute the value of p to write AB as a simplified vector in i and j.

  1. 17(−2) = −2Q → Q = 7
  2. 2AB = 7(i − 2j) = 7i − 14j

AnswerAB = 7i − 14j

Part (c) · 4 marks

Find a unit vector parallel to OA, expressed as (√a/5)(bi + cj) with integers a, b, c.

  1. 1OA = −2i − 4j
  2. 2|OA| = √((−2)² + (−4)²) = √20
  3. 3Unit vector = (1/√20)(−2i − 4j)
  4. 4= (√5/5)(−i − 2j)

Answer(√5/5)(−i − 2j)

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

Practise more unit vectors and i, j components questions

Real 4PM1 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: 4PM1 1R January 2023 · 4PM1/01R · 4pm1 jan23 1r · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.