O-LevelAdditional MathematicsVectors in two dimensions4037/21 · Oct/Nov 2011 · Q88 Marks
In the diagram OA = a, OB = b and AP = (2/5)AB. [Figure: A diagram showing vectors O, A, B, P, X. O is the origin. Vector OA is 'a', vector OB is 'b'. Point P is on line segment AB. Point X is on line OP.]
- (i)Given that OX = µOP, where µ is a constant, express OX in terms of µ, a and b.[3]
- (ii)Given also that AX = λOB, where λ is a constant, use a vector method to find the value of µ and of λ.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [1] OP = (3/5)a + (2/5)b oe
- [1] OX = µ((3/5)a + (2/5)b)
- [1] A1
- [1] OX = a + λb or AX = µ((3/5)a + (2/5)b) - a
- [1] Equates a components
- [1] µ = 5/3
- [1] Equates b components
- [1] λ = 2/3
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