OCR FP3 Specimen — Question 5

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
SessionSpecimen
TopicVectors: Cross Product & Distances

5 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations $$\frac { x - 5 } { 1 } = \frac { y - 1 } { - 1 } = \frac { z - 5 } { - 2 } \quad \text { and } \quad \frac { x - 1 } { - 4 } = \frac { y - 11 } { - 14 } = \frac { z - 2 } { 2 } .$$
  1. Find the exact value of the shortest distance between \(l _ { 1 }\) and \(l _ { 2 }\).
  2. Find an equation for the plane containing \(l _ { 1 }\) and parallel to \(l _ { 2 }\) in the form \(a x + b y + c z = d\).