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4024/21 May/Jun 2021, Question 10: Magnitude of a Vector

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Vector geometry: work with column vectors, a midpoint, and a triangle OPQ defined by p and q, finding lengths, coordinates and vector expressions.

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

Part (ai) · 2 marks

Work out the magnitude of the vector AB given as the column vector (−3, 5).

  1. 1|AB| = √((−3)² + 5²) = √34
  2. 2= 5.830… ≈ 5.83

Answer5.83 or 5.830 to 5.831

Part (aiia) · 1 mark

Given vector AC = (6, 2) and point C at (10, −1), work out the coordinates of A.

  1. 1A = C − AC = (10 − 6, −1 − 2)
  2. 2A = (4, −3)

Answer(4, −3)

Part (aiib) · 2 marks

Given that B is the midpoint of AD, work out the coordinates of D.

  1. 1B = A + AB = (4 − 3, −3 + 5) = (1, 2)
  2. 2D = B + AB = (1 − 3, 2 + 5)
  3. 3D = (−2, 7)

Answer(−2, 7)

Part (bi) · 1 mark

Using OP = p and OQ = q, write down the vector PQ in terms of p and q.

  1. 1PQ = PO + OQ = −p + q = q − p

Answerq − p

Part (bii) · 2 marks

With S the midpoint of PQ, express the vector OS in terms of p and q.

  1. 1OS = OP + 1/2 PQ = p + 1/2(q − p)
  2. 2= (1/2)p + (1/2)q

Answer(1/2)p + (1/2)q

Part (biii) · 2 marks

Given OR = 2RQ on OQ, express the vector SR in terms of p and q.

  1. 1OR = 2/3 q
  2. 2SR = SO + OR = −(1/2)p − (1/2)q + (2/3)q
  3. 3= (1/6)q − (1/2)p

Answer(1/6)q − (1/2)p

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Also searched as: 4024/21/M/J/21 · 4024_s21_qp_21 · 4024 s21 21 · question 10.
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