10 The equations of two lines \(l\) and \(m\) are \(\mathbf { r } = 3 \mathbf { i } - \mathbf { j } - 2 \mathbf { k } + \lambda ( - \mathbf { i } + \mathbf { j } + 4 \mathbf { k } )\) and \(\mathbf { r } = 4 \mathbf { i } + 4 \mathbf { j } - 3 \mathbf { k } + \mu ( 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k } )\) respectively.

1. Show that the lines do not intersect.
2. Calculate the acute angle between the directions of the lines.
3. Find the equation of the plane which passes through the point \(( 3 , - 2 , - 1 )\) and which is parallel to both \(l\) and \(m\). Give your answer in the form \(a x + b y + c z = d\).