OCR FP3 2010 June — Question 7

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2010
SessionJune
TopicVectors: Cross Product & Distances

7 A line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { r } - 7
- 3
0 \end{array} \right) + \lambda \left( \begin{array} { r } 2
- 2
3 \end{array} \right)\). A plane \(\Pi\) passes through the points \(( 1,3,5 )\) and ( \(5,2,5\) ), and is parallel to \(l\).
  1. Find an equation of \(\Pi\), giving your answer in the form r.n \(= p\).
  2. Find the distance between \(l\) and \(\Pi\).
  3. Find an equation of the line which is the reflection of \(l\) in \(\Pi\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + t \mathbf { b }\).