OCR Further Pure Core 2 2023 June — Question 6

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2023
SessionJune
TopicVectors: Lines & Planes

6 The equation of the plane \(\Pi\) is \(\mathbf { r } = \left( \begin{array} { r } - 1
2
1 \end{array} \right) + \lambda \left( \begin{array} { l } 4
4
3 \end{array} \right) + \mu \left( \begin{array} { r } - 2
3
1 \end{array} \right)\).
  1. Find the acute angle between \(\Pi\) and the plane with equation \(\mathbf { r } . \left( \begin{array} { l } 2
    0
    3 \end{array} \right) = 4\). The point \(A\) has coordinates ( \(9 , - 7,20\) ).
    The point \(F\) is the point of intersection between \(\Pi\) and the perpendicular from \(A\) to \(\Pi\).
  2. Determine the coordinates of \(F\).