AQA Further Paper 1 2024 June — Question 12 4 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2024
SessionJune
Marks4
TopicVectors: Lines & Planes

12 The line \(L _ { 1 }\) has equation $$\mathbf { r } = \left[ \begin{array} { l } 4
2
1 \end{array} \right] + \lambda \left[ \begin{array} { r } 1
3
- 1 \end{array} \right]$$ The transformation T is represented by the matrix $$\left[ \begin{array} { c c c } 2 & 1 & 0
3 & 4 & 6
- 5 & 2 & - 3 \end{array} \right]$$ The transformation T transforms the line \(L _ { 1 }\) to the line \(L _ { 2 }\) 12
  1. Show that the angle between \(L _ { 1 }\) and \(L _ { 2 }\) is 0.701 radians, correct to three decimal places.
    [0pt] [4 marks]
    12
  2. Find the shortest distance between \(L _ { 1 }\) and \(L _ { 2 }\)
    Give your answer in an exact form.