2026 DSS P2 Q4

2026 DSS P2 Q4

Secondary 4
6 marks

\(OABC\) is a trapezium. \(OC\) is parallel to \(AB\) and \(D\) is the midpoint of \(OC\).

\(\overrightarrow{OA}=4\mathbf m\) and \(\overrightarrow{OD}=3\mathbf n\). \(3AB=2OD\).

  1. Express \(\overrightarrow{OB}\), as simply as possible, in terms of \(\mathbf m\) and \(\mathbf n\).[2]
  2. \(T\) is a point on \(AD\) such that \(AT:AD=2:5\).
    Show that \(O,T\) and \(B\) are collinear.[4]

Solution:

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Answer:(a) \(4\mathbf m+2\mathbf n\). (b) \(\overrightarrow{OT}=\frac35\overrightarrow{OB}\).

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