Edexcel F3 2023 June — Question 4

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

  1. The plane \(\Pi _ { 1 }\) contains the point \(A ( 2,4 , - 5 )\) and is normal to the vector \(\left( \begin{array} { r } - 1
    3
    3 \end{array} \right)\)
The plane \(\Pi _ { 2 }\) contains the point \(B ( 3,6 , - 2 )\) and is normal to the vector \(\left( \begin{array} { r } 2
0
- 5 \end{array} \right)\)
The line \(l\) is the line of intersection of \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\)
  1. Determine a vector equation for \(l\). The points \(C\) and \(D\) both lie on \(l\).
    Given that \(C\) and \(D\) are 5 units apart,
  2. determine the exact volume of the tetrahedron \(A B C D\).