OCR Further Pure Core 2 2017 Specimen — Question 6

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2017
SessionSpecimen
TopicVectors: Lines & Planes

6 The equation of a plane \(\Pi\) is \(x - 2 y - z = 30\).
  1. Find the acute angle between the line \(\mathbf { r } = \left( \begin{array} { c } 3
    2
    - 5 \end{array} \right) + \lambda \left( \begin{array} { r } - 5
    3
    2 \end{array} \right)\) and \(\Pi\).
  2. Determine the geometrical relationship between the line \(\mathbf { r } = \left( \begin{array} { l } 1
    4
    2 \end{array} \right) + \mu \left( \begin{array} { r } 3
    - 1
    5 \end{array} \right)\) and \(\Pi\).