1. The line \(l _ { 1 }\) has equation

$$\mathbf { r } = \mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k } + \lambda ( 2 \mathbf { i } + \mathbf { j } - 4 \mathbf { k } )$$ and the line \(l _ { 2 }\) has equation $$\mathbf { r } = 5 \mathbf { i } + p \mathbf { j } - 7 \mathbf { k } + \mu ( 6 \mathbf { i } + \mathbf { j } + 8 \mathbf { k } )$$ where \(\lambda\) and \(\mu\) are scalar parameters and \(p\) is a constant.
The plane \(\Pi\) contains \(l _ { 1 }\) and \(l _ { 2 }\)

1. Show that the vector \(3 \mathbf { i } - 10 \mathbf { j } - \mathbf { k }\) is perpendicular to \(\Pi\)
2. Hence determine a Cartesian equation of \(\Pi\)
3. Hence determine the value of \(p\) Given that
   • the lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(A\)
   • the point \(B\) has coordinates \(( 12 , - 11,6 )\)
   • determine, to the nearest degree, the acute angle between \(A B\) and \(\Pi\)