1 Three planes \(P , Q\) and \(R\) have the following equations. $$\begin{array} { l l } \text { Plane } P : & 8 x - y - 14 z = 20
\text { Plane } Q : & 6 x + 2 y - 5 z = 26
\text { Plane } R : & 2 x + y - z = 40 \end{array}$$ The line of intersection of the planes \(P\) and \(Q\) is \(K\).
The line of intersection of the planes \(P\) and \(R\) is \(L\).

1. Show that \(K\) and \(L\) are parallel lines, and find the shortest distance between them.
2. Show that the shortest distance between the line \(K\) and the plane \(R\) is \(5 \sqrt { 6 }\). The line \(M\) has equation \(\mathbf { r } = ( \mathbf { i } - 4 \mathbf { j } ) + \lambda ( 5 \mathbf { i } - 4 \mathbf { j } + 3 \mathbf { k } )\).
3. Show that the lines \(K\) and \(M\) intersect, and find the coordinates of the point of intersection.
4. Find the shortest distance between the lines \(L\) and \(M\).