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A-LevelMathematicsVectors9709/12 · Oct/Nov 2011 · Q37 Marks

Relative to an origin O, the position vectors of points A and B are given by OĀ = 5i + j + 2k and OB = 2i + 7j + pk, where p is a constant.

  1. (i)Find the value of p for which angle AOB is 90°.[3]
  2. (ii)In the case where p = 4, find the vector which has magnitude 28 and is in the same direction as AB.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [3] OA.OB = 10 + 7 + 2p
  2. [3] = 0 → p = -8½
  3. [4] AB = -3i + 6j + 2k
  4. [4] Modulus = √(9+36+4)
  5. [4] Magnitude 28 → 28 ×unit vector
  6. [4] → -12i + 24j + 8k.

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About this question

Topic
Vectors, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2011 Paper 1 Variant 2, question 3.

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