CAIE FP1 2019 June — Question 7

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2019
SessionJune
TopicVectors: Cross Product & Distances

7 The line \(l _ { 1 }\) passes through the points \(A ( - 3,1,4 )\) and \(B ( - 1,5,9 )\). The line \(l _ { 2 }\) passes through the points \(C ( - 2,6,5 )\) and \(D ( - 1,7,5 )\).
  1. Find the shortest distance between the lines \(l _ { 1 }\) and \(l _ { 2 }\).
  2. Find the acute angle between the line \(l _ { 2 }\) and the plane containing \(A , B\) and \(D\).