OCR C4 2012 January — Question 7 3 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2012
SessionJanuary
Marks3
TopicVectors 3D & Lines

7 The equation of a straight line \(l\) is $$\mathbf { r } = \left( \begin{array} { l } 1
0
2 \end{array} \right) + t \left( \begin{array} { r } 1
- 1
0 \end{array} \right) .$$ \(O\) is the origin.
  1. Find the position vector of the point \(P\) on \(l\) such that \(O P\) is perpendicular to \(l\).
  2. A point \(Q\) on \(l\) is such that the length of \(O Q\) is 3 units. Find the two possible position vectors of \(Q\). [3]