Higher June 2023 Paper 2 Q20
20 \(ORT\) is a triangle.
\(\overrightarrow{OT} = \mathbf{a}\) \(\overrightarrow{RT} = \mathbf{b}\)
\(M\) is the point on \(OR\) such that \(OM : MR = 2 : 3\)
Express \(\overrightarrow{MT}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).
Give your answer in its simplest form. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{3}{5}\mathbf{a} + \dfrac{2}{5}\mathbf{b}\) | P1 | for process to find \(\overrightarrow{OR} = \mathbf{a} - \mathbf{b}\) or \(\overrightarrow{RO} = \mathbf{b} - \mathbf{a}\) |
| P1 | for process to find \(\overrightarrow{MR} = \dfrac{3}{5}(\mathbf{a} - \mathbf{b})\) or \(\overrightarrow{MO} = \dfrac{2}{5}(\mathbf{b} - \mathbf{a})\) or \(\overrightarrow{RM} = \dfrac{3}{5}(\mathbf{b} - \mathbf{a})\) or \(\overrightarrow{OM} = \dfrac{2}{5}(\mathbf{a} - \mathbf{b})\) | |
| P1 | for complete process to find \(\overrightarrow{MT}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\), eg \(\dfrac{3}{5}(\mathbf{a} - \mathbf{b}) + \mathbf{b}\) oe or \(\dfrac{2}{5}(\mathbf{b} - \mathbf{a}) + \mathbf{a}\) oe | |
| A1 | for \(\dfrac{3}{5}\mathbf{a} + \dfrac{2}{5}\mathbf{b}\) or \(\dfrac{1}{5}(3\mathbf{a} + 2\mathbf{b})\) or \(\dfrac{3\mathbf{a} + 2\mathbf{b}}{5}\) |
Additional guidance
Accept decimals instead of fractions