CAIE P3 2012 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionJune
TopicVectors: Cross Product & Distances

8 The point \(P\) has coordinates \(( - 1,4,11 )\) and the line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { r } 1
3
- 4 \end{array} \right) + \lambda \left( \begin{array} { l } 2
1
3 \end{array} \right)\).
  1. Find the perpendicular distance from \(P\) to \(l\).
  2. Find the equation of the plane which contains \(P\) and \(l\), giving your answer in the form \(a x + b y + c z = d\), where \(a , b , c\) and \(d\) are integers.