OCR FP3 2015 June — Question 3

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2015
SessionJune
TopicVectors: Lines & Planes

3 The plane \(\Pi\) passes through the points \(( 1,2,1 ) , ( 2,3,6 )\) and \(( 4 , - 1,2 )\).
  1. Find a cartesian equation of the plane \(\Pi\). The line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { r } - 1
    - 2
    6 \end{array} \right) + \lambda \left( \begin{array} { r } 4
    3
    - 2 \end{array} \right)\).
  2. Find the coordinates of the point of intersection of \(\Pi\) and \(l\).
  3. Find the acute angle between \(\Pi\) and \(l\).