11 The line \(l _ { 1 }\) passes through the point \(A\), whose position vector is \(3 \mathbf { i } - 5 \mathbf { j } - 4 \mathbf { k }\), and is parallel to the vector \(3 \mathbf { i } + 4 \mathbf { j } + 2 \mathbf { k }\). The line \(l _ { 2 }\) passes through the point \(B\), whose position vector is \(2 \mathbf { i } + 3 \mathbf { j } + 5 \mathbf { k }\), and is parallel to the vector \(\mathbf { i } - \mathbf { j } - 4 \mathbf { k }\). 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 \(l _ { 2 }\). The plane \(\Pi _ { 1 }\) contains \(P Q\) and \(l _ { 1 }\), and the plane \(\Pi _ { 2 }\) contains \(P Q\) and \(l _ { 2 }\).

1. Find the length of \(P Q\).
2. Find a vector perpendicular to \(\Pi _ { 1 }\).
3. Find the perpendicular distance from \(B\) to \(\Pi _ { 1 }\).
4. Find the angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).