8 The position vectors of points \(A\) and \(B\), relative to an origin \(O\), are given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
6
- 2
- 6
\end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r }
3
k
- 3
\end{array} \right)$$
where \(k\) is a constant.
- Find the value of \(k\) for which angle \(A O B\) is \(90 ^ { \circ }\).
- Find the values of \(k\) for which the lengths of \(O A\) and \(O B\) are equal.
The point \(C\) is such that \(\overrightarrow { A C } = 2 \overrightarrow { C B }\). - In the case where \(k = 4\), find the unit vector in the direction of \(\overrightarrow { O C }\).