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A-LevelMathematicsVectors9709/12 · May/June 2015 · Q99 Marks

Relative to an origin O, the position vectors of points A and B are given by OA = 2i + 4j + 4k and OB = 3i + j + 4k.

  1. (i)Use a vector method to find angle AOB.[4]
  2. (ii)The point C is such that AB = BC. Find the unit vector in the direction of OC.[4]
  3. (iii)Show that triangle OAC is isosceles.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [M1] (i) OA . OB = 6 + 4 + 16 = 26 Must be numerical at some stage
  2. [M1] (i) |OA| = √36, |OB| = √26 Product of 2 moduli
  3. [M1] (i) Cos AOB = 26 / (6√26) All linked correctly
  4. [A1] (i) → 31.8° co
  5. [B1] (ii) AB = b – a = (1 -3 0)
  6. [M1] (ii) OC = OA + 2AB or OB + AB Correct link
  7. [M1 A1] (ii) Unit vector ÷ modulus → (1/6)(4 -2 4) ÷ by modulus. co
  8. [B1] (iii) |OC| = 6, |OA| = 6 co

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About this question

Topic
Vectors, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, May/June 2015 Paper 1 Variant 2, question 9.

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