6 Lines \(l _ { 1 }\) and \(l _ { 2 }\) have vector equations $$\mathbf { r } = \mathbf { j } + \mathbf { k } + t ( 2 \mathbf { i } + a \mathbf { j } + \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = 3 \mathbf { i } - \mathbf { k } + s ( 2 \mathbf { i } + 2 \mathbf { j } - 6 \mathbf { k } )$$ respectively, where \(t\) and \(s\) are parameters and \(a\) is a constant.

1. Given that \(l _ { 1 }\) and \(l _ { 2 }\) are perpendicular, find the value of \(a\).
2. Given instead that \(l _ { 1 }\) and \(l _ { 2 }\) intersect, find
   (a) the value of \(a\),
   (b) the angle between the lines.