1MA0 Higher June 2013 Paper 1 Q27
27
Diagram NOT accurately drawn
\(PQRS\) is a parallelogram.
\(N\) is the point on \(SQ\) such that \(SN : NQ = 3 : 2\)
\(\overrightarrow{PQ} = \mathbf{a}\)
\(\overrightarrow{PS} = \mathbf{b}\)
(a) Write down, in terms of \(\mathbf{a}\) and \(\mathbf{b}\), an expression for \(\overrightarrow{SQ}\). (1)
(b) Express \(\overrightarrow{NR}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\). (3)
| Answer | Mark | Notes |
|---|---|---|
| \(\mathbf{a} - \mathbf{b}\) | 1 | B1 for \(\mathbf{a} - \mathbf{b}\) oe |
| Answer | Mark | Notes |
|---|---|---|
| \(\frac{2}{5}\mathbf{a} + \frac{3}{5}\mathbf{b}\) | 3 | M1 for a correct vector statement for \(\overrightarrow{NR}\) eg. (\(\overrightarrow{NR} =\)) \(\overrightarrow{NQ} + \overrightarrow{QR}\) or (\(\overrightarrow{NR} =\)) \(\overrightarrow{NS} + \overrightarrow{SR}\) M1 for \(\frac{2}{5}SQ\) (+ \(QR\)) or \(\frac{3}{5}QS\) (+ \(SR\)) (\(SQ\), \(QR\), \(QS\), \(SR\) may be written in terms of \(\mathbf{a}\) and \(\mathbf{b}\)) A1 for \(\frac{2}{5}(\mathbf{a} - \mathbf{b}) + \mathbf{b}\) oe or \(\frac{3}{5}(\mathbf{b} - \mathbf{a}) + \mathbf{a}\) oe |