9 Relative to an origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
8
- 6
5
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
- 10
3
- 13
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r }
2
- 3
- 1
\end{array} \right)$$
A fourth point, \(D\), is such that the magnitudes \(| \overrightarrow { A B } | , | \overrightarrow { B C } |\) and \(| \overrightarrow { C D } |\) are the first, second and third terms respectively of a geometric progression.
- Find the magnitudes \(| \overrightarrow { A B } | , | \overrightarrow { B C } |\) and \(| \overrightarrow { C D } |\).
- Given that \(D\) is a point lying on the line through \(B\) and \(C\), find the two possible position vectors of the point \(D\).