1MA0 Higher June 2015 Paper 2 Q27
27
Diagram NOT accurately drawn
\(ABC\) is a straight line.
\(AB : BC = 2 : 5\)
\(\overrightarrow{OA} = 2\mathbf{a} + \mathbf{b}\)
\(\overrightarrow{OB} = 3\mathbf{a} + 2\mathbf{b}\)
Express \(\overrightarrow{OC}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).
Give your answer in its simplest form. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB}\) \(= \mathbf{a} + \mathbf{b}\) \(\overrightarrow{AC} = \tfrac{7}{2}\overrightarrow{AB}\) \(\overrightarrow{OC} = \overrightarrow{OA} + \overrightarrow{AC}\) \(= 2\mathbf{a} + \mathbf{b} + \tfrac{7}{2}(\mathbf{a} + \mathbf{b})\) | \(\tfrac{11}{2}\mathbf{a} + \tfrac{9}{2}\mathbf{b}\) | 4 | M1 for \(\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB}\) \((= -(2\mathbf{a} + \mathbf{b}) + (3\mathbf{a} + 2\mathbf{b}))\) or \(\mathbf{a} + \mathbf{b}\) M1 for \(\overrightarrow{AC} = \tfrac{7}{2}\overrightarrow{AB}\) or \(\overrightarrow{BC} = \tfrac{5}{2}\overrightarrow{AB}\), may be in terms of \(\mathbf{a}\) and \(\mathbf{b}\) M1 (dep M2) for complete method to find \(\overrightarrow{OC}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\) A1 for \(\tfrac{11}{2}\mathbf{a} + \tfrac{9}{2}\mathbf{b}\) or equivalent simplest form (SC B2 for \(\tfrac{11}{2}\mathbf{a} + \tfrac{23}{2}\mathbf{b}\) or \(\tfrac{11}{2}\mathbf{a} + \tfrac{19}{2}\mathbf{b}\)) |