2026 PHS P1 Q24

\(ABCD\) is a parallelogram.

\(Q\) is the midpoint of \(AC\) and \(P\) is the midpoint of \(AQ\).

\(R\) is the point on \(AB\) such that \(AR=2RB\).

\(\overrightarrow{AD}=\mathbf a\) and \(\overrightarrow{AB}=3\mathbf b\).

1. Express \(\overrightarrow{DP}\), as simply as possible, in terms of \(\mathbf a\) and \(\mathbf b\).[2]
2. Explain why \(\overrightarrow{DP}\) is parallel to \(\overrightarrow{QR}\).[2]