CAIE P1 2004 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2004
SessionNovember
TopicVectors: Lines & Planes

8 The points \(A\) and \(B\) have position vectors \(\mathbf { i } + 7 \mathbf { j } + 2 \mathbf { k }\) and \(- 5 \mathbf { i } + 5 \mathbf { j } + 6 \mathbf { k }\) respectively, relative to an origin \(O\).
  1. Use a scalar product to calculate angle \(A O B\), giving your answer in radians correct to 3 significant figures.
  2. The point \(C\) is such that \(\overrightarrow { A B } = 2 \overrightarrow { B C }\). Find the unit vector in the direction of \(\overrightarrow { O C }\).