2025 CCHY PRELIMS P1 Q25

The position vectors of \(A\) and \(B\), relative to \(O\), are \(\mathbf a\) and \(\mathbf b\) respectively. \(\overrightarrow{GB}=3\overrightarrow{OB}\) and \(\overrightarrow{GA}=\dfrac12\overrightarrow{GH}\).

1. Express each of the following in terms of \(\mathbf a\) and \(\mathbf b\).
   1. \(\overrightarrow{GA}\)[1]
   2. \(\overrightarrow{HB}\)[2]
2. Use your answer to (a)(ii) to explain why \(OAHB\) is not a trapezium.[1]
3. Find the ratio of
   1. \(\dfrac{\text{area of triangle}\hspace{0.5em}OHB}{\text{area of triangle}\hspace{0.5em}GHO}\),[1]
   2. \(\dfrac{\text{area of triangle}\hspace{0.5em}OHA}{\text{area of}\hspace{0.5em}OAHB}\).[2]