OCR Pure 1 2017 Specimen — Question 2

Exam BoardOCR
ModulePure 1 (Pure Mathematics 1)
Year2017
SessionSpecimen
TopicVectors 3D & Lines

2 The points \(\mathrm { A } , \mathrm { B }\) and C have position vectors \(3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k } , - \mathbf { i } + 6 \mathbf { k }\) and \(7 \mathbf { i } - 4 \mathbf { j } - 2 \mathbf { k }\) respectively. M is the midpoint of BC .
  1. Show that the magnitude of \(\overrightarrow { O M }\) is equal to \(\sqrt { 17 }\). Point D is such that \(\overrightarrow { B C } = \overrightarrow { A D }\).
  2. Show that position vector of the point D is \(11 \mathbf { i } - 8 \mathbf { j } - 6 \mathbf { k }\).