10 The points \(A\) and \(B\) have position vectors, relative to the origin \(O\), given by $$\overrightarrow { O A } = \left( \begin{array} { r } - 1
3
5 \end{array} \right) \quad \text { and } \quad \overrightarrow { O B } = \left( \begin{array} { r } 3
- 1
- 4 \end{array} \right) .$$ The line \(l\) passes through \(A\) and is parallel to \(O B\). The point \(N\) is the foot of the perpendicular from \(B\) to \(l\).

1. State a vector equation for the line \(l\).
2. Find the position vector of \(N\) and show that \(B N = 3\).
3. Find the equation of the plane containing \(A , B\) and \(N\), giving your answer in the form \(a x + b y + c z = d\).