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O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2016 · Q77 Marks

O, P, Q and R are four points such that OP = p, OQ = q and OR = 3q - 2p.

  1. (i)(a)Find, in terms of p and q, PO.[1]
  2. (i)(b)Find, in terms of p and q, QR.[1]
  3. (ii)Justifying your answer, what can be said about the positions of the points P, Q and R?[2]
  4. (iii)Given that OP = i + 3j and that OQ = 2i + j, find the unit vector in the direction OR.[3]

Mark scheme

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

  1. [B1] q - p
  2. [B1] 2q-2p or 2(q-p)
  3. [B1] The points are collinear oe
  4. [B1] PQ is a (scalar) multiple of QR and they have a point in common. oe Condone PQ is parallel to QR and ...
  5. [B1] [ OR =] 4i – 3j oe soi
  6. [M1] √4² +(-3)² (=5) condone √4² + 3²; may be implied by correct answer or correct FT answer
  7. [A1] 1/5 (4i – 3j) oe

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2016 Paper 2 Variant 1, question 7.

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