CAIE P1 2009 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2009
SessionNovember
TopicVectors: Lines & Planes

9 Relative to an origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by $$\overrightarrow { O A } = \left( \begin{array} { r } 2
3
- 6 \end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r } 0
- 6
8 \end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r } - 2
5
- 2 \end{array} \right)$$
  1. Find angle \(A O B\).
  2. Find the vector which is in the same direction as \(\overrightarrow { A C }\) and has magnitude 30 .
  3. Find the value of the constant \(p\) for which \(\overrightarrow { O A } + p \overrightarrow { O B }\) is perpendicular to \(\overrightarrow { O C }\).