2026 SPS P2 Q8

In the diagram, \(\overrightarrow{OA}=3\mathbf a,\overrightarrow{OB}=2\mathbf b,\overrightarrow{AP}=1.5\mathbf a+\mathbf b,\overrightarrow{PQ}=k\mathbf b\) and \(\overrightarrow{BR}=h\mathbf a\), where \(k\) and \(h\) are constants.

1. Find, in terms of \(\mathbf a\) and/or \(\mathbf b\),
   1. \(\overrightarrow{AB}\)[1]
   2. \(\overrightarrow{BP}\)[1]
2. The points B, R and Q are collinear. Find the value of \(k\).[2]
3. Given that \(\overrightarrow{PR}\) is parallel to \(\overrightarrow{AB}\), show that \(h=3\).[3]
4. Find BR : RQ, and hence describe the position of R on BQ.[2]
5. Given that the area of triangle AOB is \(60\text{ units}^2\), find the area of triangle ABR.[2]