2025 MSHS PRELIMS P1 Q24

The diagram is not drawn to scale. \(\overrightarrow{AC}=6\overrightarrow{AO}\) and \(AX:XB=1:4\). \(ABCD\) is a parallelogram and \(AOC\) is its diagonal. The position vectors of \(C\) and \(D\), relative to \(O\), are \(5\mathbf b\) and \(\mathbf a\) respectively.

Express each of the following in terms of (mathbf a) and (mathbf b).

1. \(\overrightarrow{AD}\),[1]
2. \(\overrightarrow{AX}\),[2]
3. the position vector of \(X\).[2]