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4PM1/02R Jun 2023, Question 4: Unit Vectors and i, j Components

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks

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The question, in short

Use given position vectors OA = 5i + 7j and AB = ai + 16j with |OB| = 5√29 to find possible a, then a unit vector along AB.

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

Part (a) · 4 marks

Calculate the possible values of the scalar a using the vector sum OB = OA + AB and the given magnitude.

  1. 1OB = OA + AB = (5 + a)i + 23j
  2. 2(5√29)² = (5 + a)² + 23²
  3. 3725 − 529 = (5 + a)² = 196
  4. 45 + a = ±14, so a = 9 or a = −19

Answera = 9 or a = −19

Part (b) · 2 marks

Given a > 0, work out a unit vector parallel to AB.

  1. 1AB = 9i + 16j
  2. 2|AB| = √(81 + 256) = √337
  3. 3Unit vector = (1/√337)(9i + 16j)

Answer(1/√337)(9i + 16j)

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