CAIE P1 2012 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicVectors: Lines & Planes

8
  1. Find the angle between the vectors \(3 \mathbf { i } - 4 \mathbf { k }\) and \(2 \mathbf { i } + 3 \mathbf { j } - 6 \mathbf { k }\). The vector \(\overrightarrow { O A }\) has a magnitude of 15 units and is in the same direction as the vector \(3 \mathbf { i } - 4 \mathbf { k }\). The vector \(\overrightarrow { O B }\) has a magnitude of 14 units and is in the same direction as the vector \(2 \mathbf { i } + 3 \mathbf { j } - 6 \mathbf { k }\).
  2. Express \(\overrightarrow { O A }\) and \(\overrightarrow { O B }\) in terms of \(\mathbf { i } , \mathbf { j }\) and \(\mathbf { k }\).
  3. Find the unit vector in the direction of \(\overrightarrow { A B }\).