CAIE P3 2015 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2015
SessionJune
TopicVectors: Lines & Planes

6 The straight line \(l _ { 1 }\) passes through the points \(( 0,1,5 )\) and \(( 2 , - 2,1 )\). The straight line \(l _ { 2 }\) has equation \(\mathbf { r } = 7 \mathbf { i } + \mathbf { j } + \mathbf { k } + \mu ( \mathbf { i } + 2 \mathbf { j } + 5 \mathbf { k } )\).
  1. Show that the lines \(l _ { 1 }\) and \(l _ { 2 }\) are skew.
  2. Find the acute angle between the direction of the line \(l _ { 2 }\) and the direction of the \(x\)-axis.