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4024/22 Oct/Nov 2020, Question 8: Magnitude of a Vector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

Use vector HJ from point H to find its length and a point K, then use a parallelogram diagram with p and q to express three vectors.

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

Part (ai) · 2 marks

Find the length of the vector HJ given its column vector.

  1. 1|→HJ| = √(10² + (−6)²) = √136
  2. 2= 11.66… ≈ 11.7

Answer11.7 or 11.66...

Part (aii) · 2 marks

Find the coordinates of K, where vector HK is 3 times vector HJ.

  1. 1→HK = 3 × column vector (10, −6) = column vector (30, −18)
  2. 2K = (−7 + 30, 4 − 18) = (23, −14)

Answer(23, −14)

Part (bi) · 1 mark

Express vector OC in terms of p and q using the parallelogram.

  1. 1OA : AB = 1 : 3, so →OB = 4p
  2. 2→OC = →OB + →BC = 4p + q

Answer4p + q

Part (bii) · 2 marks

Express vector AX in terms of p and q, using the given ratio on OB.

  1. 1OA : AB = 1 : 3, so →AB = 3p
  2. 2BC is parallel and equal to OE, so →BC = q
  3. 3BX : XC = 3 : 2, so →BX = 3/5 q
  4. 4→AX = →AB + →BX = 3p + 3/5 q

Answer3p + 3/5 q

Part (biii) · 2 marks

Express vector EX in terms of p and q, using the ratio on BC.

  1. 1EC is parallel and equal to OB, so →EC = p + 3p = 4p
  2. 2BX : XC = 3 : 2, so XC is 2/5 of BC: →CX = −2/5 q
  3. 3→EX = →EC + →CX = 4p − 2/5 q

Answer4p − 2/5 q

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Also searched as: 4024/22/O/N/20 · 4024_w20_qp_22 · 4024 w20 22 · question 8.
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