2026 IGCSE Additional Mathematics May/June 0606/11 Q11

A triangle \(OAB\) is such that \(\overrightarrow{OA}=\mathbf{a}\) and \(\overrightarrow{OB}=\mathbf{b}\).

The point \(X\) lies on \(OA\) such that \(\overrightarrow{OA}=3\overrightarrow{OX}\).

The point \(Y\) lies on \(XB\) such that \(\overrightarrow{XB}=5\overrightarrow{XY}\).

The point \(Z\) lies on \(OB\) such that \(\overrightarrow{OB}=m\overrightarrow{OZ}\), where \(m\) is a scalar.

\(\overrightarrow{OX}=n\overrightarrow{ZY}\), where \(n\) is a scalar.

Use a vector method to find the values of \(m\) and \(n\).[8]