10 The line \(l _ { 1 }\) is parallel to the vector \(\mathbf { i } - 2 \mathbf { j } - 3 \mathbf { k }\) and passes through the point \(A\), whose position vector is \(3 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k }\). The line \(l _ { 2 }\) is parallel to the vector \(- 2 \mathbf { i } + \mathbf { j } + 3 \mathbf { k }\) and passes through the point \(B\), whose position vector is \(- 3 \mathbf { i } - \mathbf { j } + 2 \mathbf { k }\). 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 \(l _ { 2 }\). Find

1. the length \(P Q\),
2. the cartesian equation of the plane \(\Pi\) containing \(P Q\) and \(l _ { 2 }\),
3. the perpendicular distance of \(A\) from \(\Pi\).