9 The line \(l _ { 1 }\) passes through the point \(A\) with position vector \(\mathbf { i } - \mathbf { j } - 2 \mathbf { k }\) and is parallel to the vector \(3 \mathbf { i } - 4 \mathbf { j } - 2 \mathbf { k }\). The variable line \(l _ { 2 }\) passes through the point \(( 1 + 5 \cos t ) \mathbf { i } - ( 1 + 5 \sin t ) \mathbf { j } - 14 \mathbf { k }\), where \(0 \leqslant t < 2 \pi\), and is parallel to the vector \(15 \mathbf { i } + 8 \mathbf { j } - 3 \mathbf { k }\). The points \(P\) and \(Q\) are on \(l _ { 1 }\) and \(l _ { 2 }\) respectively, and \(P Q\) is perpendicular to both \(l _ { 1 }\) and \(l _ { 2 }\).

1. Find the length of \(P Q\) in terms of \(t\).
2. Hence show that the lines \(l _ { 1 }\) and \(l _ { 2 }\) do not intersect, and find the maximum length of \(P Q\) as \(t\) varies.
3. The plane \(\Pi _ { 1 }\) contains \(l _ { 1 }\) and \(P Q\); the plane \(\Pi _ { 2 }\) contains \(l _ { 2 }\) and \(P Q\). Find the angle between the planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\), correct to the nearest tenth of a degree.