OCR FP3 2009 June — Question 6

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2009
SessionJune
TopicVectors: Lines & Planes

6 The plane \(\Pi _ { 1 }\) has equation \(\mathbf { r } = \left( \begin{array} { l } 2
2
1 \end{array} \right) + \lambda \left( \begin{array} { l } 1
1
0 \end{array} \right) + \mu \left( \begin{array} { r } 1
- 5
- 2 \end{array} \right)\).
  1. Express the equation of \(\Pi _ { 1 }\) in the form r.n \(= p\). The plane \(\Pi _ { 2 }\) has equation \(\mathbf { r } . \left( \begin{array} { r } 7
    17
    - 3 \end{array} \right) = 21\).
  2. Find an equation of the line of intersection of \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\), giving your answer in the form \(\mathbf { r } = \mathbf { a } + t \mathbf { b }\).