10 With respect to the origin \(O\), the points \(A , B\) and \(C\) have position vectors given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
3
- 2
4
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
2
- 1
7
\end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r }
1
- 5
- 3
\end{array} \right)$$
The plane \(m\) is parallel to \(\overrightarrow { O C }\) and contains \(A\) and \(B\).
- Find the equation of \(m\), giving your answer in the form \(a x + b y + c z = d\).
- Find the length of the perpendicular from \(C\) to the line through \(A\) and \(B\).