Edexcel F3 2023 January — Question 7

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2023
SessionJanuary
TopicVectors: Lines & Planes

  1. The plane \(\Pi\) has equation
$$\mathbf { r } = \left( \begin{array} { l } 1
2
3 \end{array} \right) + \lambda \left( \begin{array} { r } 0
3
- 2 \end{array} \right) + \mu \left( \begin{array} { l } 1
1
2 \end{array} \right)$$ where \(\lambda\) and \(\mu\) are scalar parameters.
  1. Determine a vector perpendicular to \(\Pi\) The line \(l\) meets \(\Pi\) at the point ( \(1,2,3\) ) and passes through the point ( \(1,0,1\) )
  2. Determine the size of the acute angle between \(\Pi\) and \(l\) Give your answer to the nearest degree.
  3. Determine the shortest distance between \(\Pi\) and the point \(( 6 , - 3 , - 6 )\)