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0580/22 May/Jun 2023, Question 9: Magnitude of a Vector

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks

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The question, in short

Given point F (1, −4) and column vectors FG = (8, −3) and GH = (−12, 35), find a scalar multiple, a sum, point G's coordinates, and the length of GH.

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

Part (a) · 1 mark

Calculate 3 times the column vector FG, giving the resulting column vector.

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

Answercolumn vector (24, −9)

Part (b) · 1 mark

Add the column vectors FG and GH, giving the resulting column vector.

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

Answercolumn vector (−4, 32)

Part (c) · 1 mark

Use F and vector FG to work out the coordinates of point G.

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

Answer(9, −7)

Part (d) · 2 marks

Find the magnitude of the column vector GH.

  1. 1|→GH| = √((−12)² + 35²)
  2. 2= √(144 + 1225) = √1369
  3. 3= 37

Answer37

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