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0580/12 May/Jun 2023, Question 15: Multiplying a Vector by a Scalar

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 3 marks

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The question, in short

Point F is (1, −4), vector FG is (8, −3) and vector GH is (−12, 35). Find a scalar multiple of FG, the sum FG + GH, and the coordinates of G.

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

Part (a) · 1 mark

Calculate 3→FG, giving the resulting column vector.

  1. 13 × (8, −3) = column vector (24, −9)

Answercolumn vector (24, −9)

Part (b) · 1 mark

Calculate →FG + →GH as a column vector.

  1. 1(8 + (−12), −3 + 35)
  2. 2= column vector (−4, 32)

Answercolumn vector (−4, 32)

Part (c) · 1 mark

Using F and →FG, work out the coordinates of point G.

  1. 1G = F + FG = (1 + 8, −4 + (−3))
  2. 2G = (9, −7)

Answer(9, −7)

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