9 Relative to an origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
2
- 2
- 1
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
- 2
3
6
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { l }
2
6
5
\end{array} \right)$$
- Use a scalar product to find angle \(A O B\).
- Find the vector which is in the same direction as \(\overrightarrow { A C }\) and of magnitude 15 units.
- Find the value of the constant \(p\) for which \(p \overrightarrow { O A } + \overrightarrow { O C }\) is perpendicular to \(\overrightarrow { O B }\).