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0580/42 Oct/Nov 2022, Question 11: Magnitude of a Vector

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Given a vector magnitude equation with m, solve for both m values; then use a parallelogram with sides a and c and point P dividing CB in ratio 3:1 to find vectors and a meeting point Q.

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

Part (a) · 3 marks

Solve the magnitude equation for the two values of m.

  1. 1(9m)² + (40m)² = (205/2)²
  2. 21681m² = 42025/4
  3. 3m² = 6.25
  4. 4m = 2.5 and −2.5

Answer2.5 and −2.5

Part (bia) · 1 mark

Express vector AC using a and c.

  1. 1→AC = →AO + →OC = −a + c = c − a

Answerc − a

Part (bib) · 1 mark

Express vector CP using a and c.

  1. 1CB = OA = a, so →CP = 3/4 a

Answer3/4 a

Part (bic) · 1 mark

Express vector OP using a and c.

  1. 1→OP = →OC + →CP = c + 3/4 a

Answerc + 3/4 a

Part (bii) · 2 marks

Find the position vector of Q where lines OP and AB extended intersect.

  1. 1Q is on AB extended, so →OQ = a + kc
  2. 2Q is on OP extended, so →OQ = t(c + 3/4 a)
  3. 33/4 t = 1 gives t = 4/3, so k = 4/3
  4. 4→OQ = a + 4/3 c

Answera + 4/3 c

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Also searched as: 0580/42/O/N/22 · 0580_w22_qp_42 · 0580 w22 42 · question 11.
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