1MA0 Higher November 2016 Paper 2 Q23
23
Diagram NOT accurately drawn
\(OAB\) is a triangle.
\(\overrightarrow{OA} = 5\mathbf{a}\)
\(\overrightarrow{OB} = 2\mathbf{b}\)
\(T\) is the point on \(AB\) such that \(AT : TB = 5 : 1\)
Show that \(OT\) is parallel to the vector \(\mathbf{a} + 2\mathbf{b}\) (4)
| Answer | Mark | Notes |
|---|---|---|
| Correct conclusion from correct working | 4 | B1 for \(\overrightarrow{AB} = -5\mathbf{a} + 2\mathbf{b}\) or \(\overrightarrow{BA} = 5\mathbf{a} - 2\mathbf{b}\) M1 for a correct vector statement for \(\overrightarrow{OT}\) eg \(\overrightarrow{OA} + \overrightarrow{AT}\) or \(\overrightarrow{OB} + \overrightarrow{BT}\) or \(\overrightarrow{OA} + \dfrac{5}{6}\overrightarrow{AB}\) or \(\overrightarrow{OB} + \dfrac{1}{6}\overrightarrow{BA}\), may be written partially or fully in terms of \(\mathbf{a}\) and \(\mathbf{b}\) M1 for \(5\mathbf{a} + \dfrac{5}{6}(-5\mathbf{a} + 2\mathbf{b})\) oe or \(2\mathbf{b} + \dfrac{1}{6}(5\mathbf{a} - 2\mathbf{b})\) oe A1 for \(\dfrac{5}{6}(\mathbf{a} + 2\mathbf{b})\) is parallel to \(\mathbf{a} + 2\mathbf{b}\) |