OCR Further Pure Core 2 2018 December — Question 5

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2018
SessionDecember
TopicVectors 3D & Lines
5
  1. Find the shortest distance between the point ( \(- 6,4\) ) and the line \(y = - 0.75 x + 7\). Two lines, \(l _ { 1 }\) and \(l _ { 2 }\), are given by
    \(l _ { 1 } : \mathbf { r } = \left( \begin{array} { c } 4
    3
    - 2 \end{array} \right) + \lambda \left( \begin{array} { c } 2
    1
    - 4 \end{array} \right)\) and \(l _ { 2 } : \mathbf { r } = \left( \begin{array} { c } 11
    - 1
    5 \end{array} \right) + \mu \left( \begin{array} { c } 3
    - 1
    1 \end{array} \right)\).
  2. Find the shortest distance between \(l _ { 1 }\) and \(l _ { 2 }\).
  3. Hence determine the geometrical arrangement of \(l _ { 1 }\) and \(l _ { 2 }\).
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