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N2008 P1 Q3

N2008 P1 Q3

Junior College 2
6 marks

Points \(O,A,B\) are such that \(\overrightarrow{OA}=\mathbf i+4\mathbf j-3\mathbf k\) and \(\overrightarrow{OB}=5\mathbf i-\mathbf j\), and the point \(P\) is such that \(OAPB\) is a parallelogram.

  1. Find \(\overrightarrow{OP}\).[1]
  2. Find the size of angle \(AOB\).[3]
  3. Find the exact area of the parallelogram \(OAPB\).[2]

Solution:

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Answer:(i) \(6\mathbf i+3\mathbf j-3\mathbf k\). (ii) \(87.8^\circ\). (iii) \(15\sqrt3\).

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