CAIE P3 2023 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicVectors: Lines & Planes

10 The equations of the lines \(l\) and \(m\) are given by $$l : \mathbf { r } = \left( \begin{array} { r } 3
- 2
1 \end{array} \right) + \lambda \left( \begin{array} { l } 1
1
2 \end{array} \right) \quad \text { and } \quad m : \mathbf { r } = \left( \begin{array} { r } 6
- 3
6 \end{array} \right) + \mu \left( \begin{array} { r } - 2
4
c \end{array} \right)$$ where \(c\) is a positive constant. It is given that the angle between \(l\) and \(m\) is \(60 ^ { \circ }\).
  1. Find the value of \(c\).
  2. Show that the length of the perpendicular from \(( 6 , - 3,6 )\) to \(l\) is \(\sqrt { 11 }\).