9 Relative to an origin \(O\), the position vectors of the points \(A\) and \(B\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
4
1
- 2
\end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r }
3
2
- 4
\end{array} \right) .$$
- Given that \(C\) is the point such that \(\overrightarrow { A C } = 2 \overrightarrow { A B }\), find the unit vector in the direction of \(\overrightarrow { O C }\).
The position vector of the point \(D\) is given by \(\overrightarrow { O D } = \left( \begin{array} { l } 1
4
k \end{array} \right)\), where \(k\) is a constant, and it is given that \(\overrightarrow { O D } = m \overrightarrow { O A } + n \overrightarrow { O B }\), where \(m\) and \(n\) are constants. - Find the values of \(m , n\) and \(k\).