CAIE P1 2012 November — Question 9

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

9 The position vectors of points \(A\) and \(B\) relative to an origin \(O\) are \(\mathbf { a }\) and \(\mathbf { b }\) respectively. The position vectors of points \(C\) and \(D\) relative to \(O\) are \(3 \mathbf { a }\) and \(2 \mathbf { b }\) respectively. It is given that $$\mathbf { a } = \left( \begin{array} { l } 2
1
2 \end{array} \right) \quad \text { and } \quad \mathbf { b } = \left( \begin{array} { l } 4
0
6 \end{array} \right) .$$
  1. Find the unit vector in the direction of \(\overrightarrow { C D }\).
  2. The point \(E\) is the mid-point of \(C D\). Find angle \(E O D\).