O-LevelAdditional MathematicsVectors in two dimensions4037/22 · Oct/Nov 2020 · Q99 Marks
In the diagram OP = 2b, OS = 3a, SR = b and PQ = a. The lines OR and QS intersect at X. [Figure 9.1: A diagram showing vectors OP, OS, SR, PQ. Lines OR and QS intersect at X.]
- (a)Find OQ in terms of a and b.[1]
- (b)Find QS in terms of a and b.[1]
- (c)Given that QX = μQS, find OX in terms of a, b and μ.[1]
- (d)Given that OX = λOR, find OX in terms of a, b and λ.[1]
- (e)Find the value of λ and of μ.[3]
- (f)Find the value of OX / XS .[1]
- (g)Find the value of OR / OX .[1]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] (a) OQ = 2b + a
- [B1] (b) QS = 2a - 2b
- [B1] (c) OX = 2b + a + μ(2a - 2b) FT on their OQ and QS isw
- [B1] (d) OX = λ(3a + b) λ3a + λb is B0
- [M1] (e) 3λ=1+2μ for forming two simultaneous equations equating correct terms. Each equation must have 3 terms. M1Dep for attempting to solve by removing μ or λ to λ or μ =
- [A1] (e) λ = 3/4, μ = 5/8 for both
- [B1] (f) QX / XS = 5/3 FT Must be positive from μ < 1
- [B1] (g) OR / OX = 4/3 FT Must be positive from λ < 1
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