OCR C4 2010 January — Question 9

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2010
SessionJanuary
TopicVectors 3D & Lines

9 The equation of a straight line \(l\) is \(\mathbf { r } = \left( \begin{array} { l } 3
1
1 \end{array} \right) + t \left( \begin{array} { r } 1
- 1
2 \end{array} \right) . O\) is the origin.
  1. The point \(P\) on \(l\) is given by \(t = 1\). Calculate the acute angle between \(O P\) and \(l\).
  2. Find the position vector of the point \(Q\) on \(l\) such that \(O Q\) is perpendicular to \(l\).
  3. Find the length of \(O Q\).