7 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations \(\mathbf { r } = \mathbf { i } + 3 \mathbf { j } - 2 \mathbf { k } + \lambda ( 2 \mathbf { i } + \mathbf { j } + \mathbf { k } )\) and \(\mathbf { r } = \mathbf { i } - 2 \mathbf { j } + 9 \mathbf { k } + \mu ( \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k } )\) respectively. The plane \(\Pi _ { 1 }\) contains \(l _ { 1 }\) and is parallel to \(l _ { 2 }\).

1. Find the equation of \(\Pi _ { 1 }\), giving your answer in the form \(a x + b y + c z = d\).
   The plane \(\Pi _ { 2 }\) contains \(l _ { 2 }\) and the point with coordinates \(( 2 , - 1,7 )\).
2. Find the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).
   \includegraphics[max width=\textwidth, alt={}, center]{beb69d0f-3f83-49bf-b9a2-329ddc7243fa-15_2723_35_101_20} The point \(P\) on \(l _ { 1 }\) and the point \(Q\) on \(l _ { 2 }\) are such that \(P Q\) is perpendicular to both \(l _ { 1 }\) and \(l _ { 2 }\).
3. Find a vector equation for \(P Q\).
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