7. With respect to a fixed origin \(O\), the lines \(l _ { 1 }\) and \(l _ { 2 }\) are given by the equations $$\begin{aligned} & l _ { 1 } : \mathbf { r } = ( 9 \mathbf { i } + 13 \mathbf { j } - 3 \mathbf { k } ) + \lambda ( \mathbf { i } + 4 \mathbf { j } - 2 \mathbf { k } )
& l _ { 2 } : \mathbf { r } = ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } ) + \mu ( 2 \mathbf { i } + \mathbf { j } + \mathbf { k } ) \end{aligned}$$ where \(\lambda\) and \(\mu\) are scalar parameters.

1. Given that \(l _ { 1 }\) and \(l _ { 2 }\) meet, find the position vector of their point of intersection.
2. Find the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\), giving your answer in degrees to 1 decimal place. Given that the point \(A\) has position vector \(4 \mathbf { i } + 16 \mathbf { j } - 3 \mathbf { k }\) and that the point \(P\) lies on \(l _ { 1 }\) such that \(A P\) is perpendicular to \(l _ { 1 }\),
3. find the exact coordinates of \(P\).