10 Lines \(l _ { 1 }\) and \(l _ { 2 }\) have vector equations $$\mathbf { r } = - \mathbf { i } + 2 \mathbf { j } + 7 \mathbf { k } + t ( 2 \mathbf { i } + 2 \mathbf { j } + \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = 2 \mathbf { i } + 9 \mathbf { j } - 4 \mathbf { k } + s ( \mathbf { i } + 3 \mathbf { j } - 2 \mathbf { k } )$$ respectively. The point \(A\) has coordinates ( \(- 3,0,6\) ) relative to the origin \(O\).

1. Show that \(A\) lies on \(l _ { 1 }\) and that \(O A\) is perpendicular to \(l _ { 1 }\).
2. Show that the line through \(O\) and \(A\) intersects \(l _ { 2 }\).
3. Given that the point of intersection in part (ii) is \(B\), find the ratio \(| \overrightarrow { O A } | : | \overrightarrow { B A } |\). \section*{THERE ARE NO QUESTIONS WRITTEN ON THIS PAGE.}