9 The plane \(\Pi\) has equation $$\mathbf { r } = 2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k } + \lambda ( \mathbf { i } - 2 \mathbf { j } + 2 \mathbf { k } ) + \mu ( 3 \mathbf { i } + \mathbf { j } - 2 \mathbf { k } )$$ The line \(l\), which does not lie in \(\Pi\), has equation $$\mathbf { r } = 3 \mathbf { i } + 6 \mathbf { j } + 12 \mathbf { k } + t ( 8 \mathbf { i } + 5 \mathbf { j } - 8 \mathbf { k } )$$ Show that \(l\) is parallel to \(\Pi\). Find the position vector of the point at which the line with equation \(\mathbf { r } = 5 \mathbf { i } - 4 \mathbf { j } + 7 \mathbf { k } + s ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } )\) meets \(\Pi\). Find the perpendicular distance from the point with position vector \(9 \mathbf { i } + 11 \mathbf { j } + 2 \mathbf { k }\) to \(l\).