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A-LevelMathematicsVectors9709/12 · May/June 2016 · Q34 Marks

Relative to an origin O, the position vectors of points A and B are given by OA = 2i – 5j – 2k and OB = 4i – 4j + 2k. The point C is such that AB = BC. Find the unit vector in the direction of OC.

  1. Relative to an origin O, the position vectors of points A and B are given by OA = 2i – 5j – 2k and OB = 4i – 4j + 2k. The point C is such that AB = BC. Find the unit vector in the direction of OC.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

  1. [B1] AB = 2i + j +4k or AC = 4i + 2j + 8k
  2. [M1] OC = OA+ AC = 6i -3j + 6k correct method for OC
  3. OR
  4. [B1] (x-4) = 2 (y+4) = 1 (z-2) = 4
  5. [M1] OC = y= -3 z= 6
  6. OR
  7. [B1] OB – OA = OC – OB .: OC = 2OB – OA
  8. [M1] Divides by their mod of their OC
  9. [A1] = (6i -3j + 6k) ÷ 9 Correct unsimplified expression

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About this question

Topic
Vectors, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, May/June 2016 Paper 1 Variant 2, question 3.

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