OCR C4 2013 January — Question 4

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2013
SessionJanuary
TopicVectors 3D & Lines

4 The equations of two lines are $$\mathbf { r } = \mathbf { i } + 2 \mathbf { j } + \lambda ( 2 \mathbf { i } + \mathbf { j } + 3 \mathbf { k } ) \text { and } \mathbf { r } = 6 \mathbf { i } + 8 \mathbf { j } + \mathbf { k } + \mu ( \mathbf { i } + 4 \mathbf { j } - 5 \mathbf { k } ) .$$
  1. Show that these lines meet, and find the coordinates of the point of intersection.
  2. Find the acute angle between these lines.