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4MA1/1HR Jun 2023, Question 19: Magnitude of a Vector

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

Using vectors AB = (7, −2) and BC = (−3, 5) in km, find how much farther Pru's route A to B to C is than Yang's direct route A to C, to 1 decimal place.

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

Solution · 5 marks

  1. 1AB = (7, −2) and BC = (−3, 5)
  2. 2AC = AB + BC
  3. 3x component: 7 + (−3) = 4
  4. 4y component: −2 + 5 = 3
  5. 5So AC = (4, 3)
  6. 6Yang's distance = |AC| = √(4² + 3²) = √(16 + 9) = √25 = 5
  7. 7|AB| = √(7² + (−2)²) = √(49 + 4) = √53 = 7.280...
  8. 8|BC| = √((−3)² + 5²) = √(9 + 25) = √34 = 5.830...
  9. 9Pru's distance = 7.280... + 5.830... = 13.111...
  10. 1013.111... − 5 = 8.111...
  11. 11Pru travels 8.1 km further

Answer8.1

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