Higher November 2019 Paper 3 Q27
27 Here is quadrilateral PQRS.
\(\overrightarrow{PS}\) \(= \mathbf{a}\) \(\overrightarrow{SR}\) \(= \mathbf{b}\) \(\overrightarrow{RQ}\) \(= \mathbf{c}\)
Not drawn accurately
X is a point on PS where \(\quad PX : XS = 1 : 2\)
Y is a point on RQ where \(\quad RY : YQ = 2 : 1\)
Not drawn accurately
Is XY parallel to PQ?
Show working to support your answer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (PQ =) \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) | M1 | oe |
| (XY =) \(\dfrac{2}{3}\mathbf{a} + \mathbf{b} + \dfrac{2}{3}\mathbf{c}\) or (XY =) \(-\dfrac{1}{3}\mathbf{a} + \mathbf{a} + \mathbf{b} + \mathbf{c} - \dfrac{1}{3}\mathbf{c}\) | M1 | |
| (PQ =) \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) and (XY =) \(\dfrac{2}{3}\mathbf{a} + \mathbf{b} + \dfrac{2}{3}\mathbf{c}\) and No, as XY is not a multiple of PQ | A1 | oe |