2026 EVG P1 Q24

\(\overrightarrow{OA}=8\mathbf a\) and \(\overrightarrow{OB}=8\mathbf b\). Given \(BM=MA\) and \(\overrightarrow{OL}=\dfrac14\overrightarrow{OA}\).

1. Write each of the following in terms of \(\mathbf a\) and \(\mathbf b\), in simplest form.
   1. \(\overrightarrow{BM}\)[1]
   2. \(\overrightarrow{OM}\)[1]
   3. \(\overrightarrow{LM}\)[1]
2. Find \(\overrightarrow{OP}\) such that \(\overrightarrow{LP}=3\overrightarrow{LM}\).[2]
3. Explain why \(\overrightarrow{OP}\) is not parallel to \(\overrightarrow{OM}\).[1]
4. Find \(\dfrac{\text{Area of triangle}\hspace{0.5em}ALM}{\text{Area of triangle}\hspace{0.5em}AOB}\).[1]