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4024/22 May/Jun 2021, Question 12: Magnitude of a Vector

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

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The question, in short

Vector geometry: work with points A(2, 3), B(3, −5) and D(−3, n), then use a parallelogram diagram with vectors p and q to find a side ratio.

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

Part (ai) · 2 marks

Calculate the column vector from A to B using the given coordinates.

  1. 1AB = (3 − 2, −5 − 3)
  2. 2AB = column vector (1, −8)

Answercolumn vector (1, −8)

Part (aii) · 1 mark

Given the vector from B to C, determine where point C lies.

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

Answer(−1, −2)

Part (aiii) · 3 marks

Using the stated length of vector AD and D = (−3, n), solve for every possible n.

  1. 1(−3 − 2)² + (n − 3)² = 74
  2. 225 + (n − 3)² = 74 → (n − 3)² = 49
  3. 3n − 3 = ±7
  4. 4n = 10 or n = −4

Answer10 and −4

Part (b) · 3 marks

In parallelogram OQRP with K the midpoint of OQ and L on PR, use the given vector KL to work out the ratio PL : LR.

  1. 1KL = KO + OP + PL = −(1/2)q + p + PL
  2. 2−(1/2)q + p + PL = p − (1/10)q → PL = (2/5)q
  3. 3PR = q, so LR = (3/5)q
  4. 4PL : LR = 2 : 3

Answer2 : 3

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Also searched as: 4024/22/M/J/21 · 4024_s21_qp_22 · 4024 s21 22 · question 12.
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