2026 RSS P1 Q25

\(OAB\) is a triangle.

\(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\).

\(C\) is the point on \(AB\) such that \(AC:CB=3:1\).

\(D\) is the point on \(OB\) such that \(OD:DB=3:4\).

1. Find, in terms of \(\mathbf a\) and \(\mathbf b\),
   1. \(\overrightarrow{AB}\),[1]
   2. \(\overrightarrow{OC}\),[2]
   3. \(\overrightarrow{OD}\).[1]
2. \(Q\) is a point on \(OC\) such that \(\overrightarrow{OQ}=\dfrac18\mathbf a+\dfrac38\mathbf b\).
   1. Show that \(A\), \(Q\) and \(D\) are collinear.[3]
   2. Find the ratio of the area of triangle \(OAQ\) to the area of triangle \(ODQ\).[1]