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0580/21 May/Jun 2025, Question 8: Expressing Vectors in Terms of a and b

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks

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The question, in short

Given column vectors m = (11, 5) and n = (8, −3), compute a vector combination and find y from a magnitude condition.

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Part (a) · 2 marks

Calculate 2m − n as a column vector.

  1. 12m = column vector (22, 10)
  2. 22m − n = column vector (22 − 8, 10 − (−3))
  3. 3= column vector (14, 13)

Answercolumn vector (14, 13)

Part (b) · 2 marks

The vector (5, √y) has magnitude 7; find y.

  1. 15² + (√y)² = 7²
  2. 225 + y = 49
  3. 3y = 24

Answer24

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