2025 MGS(S) PRELIMS P1 Q22

\(S\) is the point \((1,-3)\), \(T\) is the point \((5,w)\), \(\overrightarrow{PQ}=\begin{pmatrix}1\\4\end{pmatrix}\), and \(\overrightarrow{QR}=\begin{pmatrix}8\\6\end{pmatrix}\).

1. Find \(|\overrightarrow{QR}|\).[1]
2. Express \(\overrightarrow{ST}\) as a column vector in terms of \(w\).[1]
3. Find \(w\), given that \(\overrightarrow{ST}\) is parallel to \(\overrightarrow{PQ}\).[2]