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O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2021 · Q108 Marks

Relative to an origin O, the position vectors of the points A, B, C and D are OA = (6, -3), OB = (10, 3), OC = (x, y) and OD = (12, 7)

  1. (a)Find the unit vector in the direction of AB.[3]
  2. (b)The point A is the mid-point of BC. Find the value of x and of y.[2]
  3. (c)The point E lies on OD such that OE : OD is 1 : 1 + λ. Find the value of λ such that BE is parallel to the x-axis.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [B1] AB = (4/6)
  2. [M1] √(4²+6²)
  3. [A1] 1/√52 * (4/6) oe isw (FT provided working shown)
  4. [M1] (6/-3) = 1/2 * (10+x / 3+y) oe
  5. [A1] x = 2, y = -9
  6. [B1] OE = 1/(1+λ) * (12/7) oe seen
  7. [M1] Solves their (7/(1+λ)) = 3
  8. [A1] λ = 4/3 oe
  9. [B1] (Alternative) OE = (x_E / y_E) and identifies x_E = 12/(1+λ) and y_E = 7/(1+λ)
  10. [M1] (Alternative) Finds BE in terms of λ and sets y-component to zero, leading to 7/(1+λ) - 3 = 0
  11. [A1] (Alternative) λ = 4/3

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About this question

Topic
Vectors in two dimensions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2021 Paper 2 Variant 1, question 10.

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