Edexcel P4 2022 January — Question 8

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJanuary
TopicVectors: Lines & Planes

8. With respect to a fixed origin \(O\) the points \(A\) and \(B\) have position vectors $$\left( \begin{array} { l } 6
6
2 \end{array} \right) \text { and } \left( \begin{array} { l } 6
0
7 \end{array} \right)$$ respectively. The line \(l _ { 1 }\) passes through the points \(A\) and \(B\).
  1. Write down an equation for \(l _ { 1 }\) Give your answer in the form \(\mathbf { r } = \mathbf { p } + \lambda \mathbf { q }\), where \(\lambda\) is a scalar parameter. The line \(l _ { 2 }\) has equation $$\mathbf { r } = \left( \begin{array} { l } 3
    1
    4 \end{array} \right) + \mu \left( \begin{array} { l } 1
    5