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0580/13 May/Jun 2021, Question 10: Multiplying a Vector by a Scalar

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 3 marks

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The question, in short

Given column vectors a = (3, −4) and b = (5, 2), perform vector calculations and use a given vector from L to find point M's coordinates.

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Part (ai) · 1 mark

Work out 8b, the scalar multiple of column vector b by 8.

  1. 18b = (8 × 5, 8 × 2)
  2. 2= column vector (40, 16)

Answercolumn vector (40, 16)

Part (aii) · 1 mark

Work out a − b, subtracting column vector b from a.

  1. 1a − b = (3 − 5, −4 − 2)
  2. 2= column vector (−2, −6)

Answercolumn vector (−2, −6)

Part (b) · 1 mark

Point L is (−3, 6) and vector LM is (5, −2); find the coordinates of M.

  1. 1M = (−3 + 5, 6 + (−2))
  2. 2= (2, 4)

Answer(2, 4)

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