CAIE P1 2012 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
TopicVectors 3D & Lines

7 The position vectors of the points \(A\) and \(B\), relative to an origin \(O\), are given by $$\overrightarrow { O A } = \left( \begin{array} { l } 1
0
2 \end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r } k
- k
2 k \end{array} \right)$$ where \(k\) is a constant.
  1. In the case where \(k = 2\), calculate angle \(A O B\).
  2. Find the values of \(k\) for which \(\overrightarrow { A B }\) is a unit vector.