2026 IGCSE Additional Mathematics May/June 0606/13 Q10

5 marks

The parallelogram \(OABC\) is such that \(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\).

The point \(D\) lies on \(OB\) such that \(OD:OB=1:3\).

The point \(E\) lies on \(AC\) such that \(AE:AC=2:3\).

Show that \(\overrightarrow{DE}\) is parallel to \(\overrightarrow{AB}\).[5]

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Answer:\(\overrightarrow{DE}=\dfrac13\overrightarrow{AB}\), so they are parallel.

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