2026 MSHS P1 Q27

In the diagram, \(OABC\) is a trapezium where \(OA\) is parallel to \(CB\). \(\overrightarrow{OA}=4\mathbf a\), \(\overrightarrow{OC}=3\mathbf c\) and \(CB=\dfrac34OA\). \(M\) is the midpoint of \(AB\), and \(N\) is the point on \(OC\) such that \(ON:NC=2:1\).

1. Express \(\overrightarrow{OB}\) in terms of \(\mathbf a\) and \(\mathbf c\), as simply as possible.[2]
2. Express \(\overrightarrow{MN}\) in terms of \(\mathbf a\) and \(\mathbf c\), as simply as possible.[4]
3. The area of triangle \(MNC=33.5\text{ cm}^2\). Find the area of triangle \(MNO\).[2]