CAIE P1 2013 November — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionNovember
TopicVectors 3D & Lines

4 Relative to an origin \(O\), the position vectors of points \(A\) and \(B\) are given by $$\overrightarrow { O A } = \mathbf { i } + 2 \mathbf { j } \quad \text { and } \quad \overrightarrow { O B } = 4 \mathbf { i } + p \mathbf { k } .$$
  1. In the case where \(p = 6\), find the unit vector in the direction of \(\overrightarrow { A B }\).
  2. Find the values of \(p\) for which angle \(A O B = \cos ^ { - 1 } \left( \frac { 1 } { 5 } \right)\).