OCR FP3 2013 January — Question 4

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJanuary
TopicVectors: Cross Product & Distances

4 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations $$\mathbf { r } = \left( \begin{array} { l } 1
2
1 \end{array} \right) + \lambda \left( \begin{array} { r } 2
3
- 1 \end{array} \right) \text { and } \mathbf { r } = \left( \begin{array} { l } 3
0
1 \end{array} \right) + \mu \left( \begin{array} { r } 4
- 1
- 1 \end{array} \right)$$ respectively.
  1. Find the shortest distance between the lines.
  2. Find a cartesian equation of the plane which contains \(l _ { 1 }\) and which is parallel to \(l _ { 2 }\).