1. Relative to a fixed origin \(O\), the lines \(l _ { 1 }\) and \(l _ { 2 }\) are given by the equations

$$\begin{aligned} & l _ { 1 } : \mathbf { r } = ( 3 \mathbf { i } + p \mathbf { j } + 7 \mathbf { k } ) + \lambda ( 2 \mathbf { i } - 5 \mathbf { j } + 4 \mathbf { k } )
& l _ { 2 } : \mathbf { r } = ( 8 \mathbf { i } - 2 \mathbf { j } + 5 \mathbf { k } ) + \mu ( 4 \mathbf { i } + \mathbf { j } + 2 \mathbf { k } ) \end{aligned}$$ where \(\lambda\) and \(\mu\) are scalar parameters and \(p\) is a constant.
Given that \(l _ { 1 }\) and \(l _ { 2 }\) intersect,

1. find the value of \(p\),
2. find the position vector of the point of intersection.
3. Find the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\) Give your answer in degrees to one decimal place. The point \(A\) lies on \(l _ { 1 }\) with parameter \(\lambda = 2\)
   The point \(B\) lies on \(l _ { 2 }\) with \(\overrightarrow { A B }\) perpendicular to \(l _ { 2 }\)
4. Find the coordinates of \(B\)