2026 NASS P1 Q26

\(ABCD\) is a quadrilateral.

\(E\) is the point on \(BD\) such that \(BE:BD=3:4\).

\(F\) is the midpoint of \(BC\).

\(\overrightarrow{AB}=4\mathbf a\), \(\overrightarrow{AD}=8\mathbf b\) and \(\overrightarrow{EF}=2(\mathbf a-\mathbf b)\).

1. Express \(\overrightarrow{BE}\) in terms of \(\mathbf a\) and \(\mathbf b\), as simply as possible.[2]
2. Express \(\overrightarrow{BC}\) in terms of \(\mathbf a\) and \(\mathbf b\), as simply as possible.[2]
3. What type of quadrilateral is \(ABCD\)?
   Explain your answer using vectors.[3]