1 The point \(\mathrm { A } ( - 1,12,5 )\) lies on the plane \(P\) with equation \(8 x - 3 y + 10 z = 6\). The point \(\mathrm { B } ( 6 , - 2,9 )\) lies on the plane \(Q\) with equation \(3 x - 4 y - 2 z = 8\). The planes \(P\) and \(Q\) intersect in the line \(L\).

1. Find an equation for the line \(L\).
2. Find the shortest distance between \(L\) and the line AB . The lines \(M\) and \(N\) are both parallel to \(L\), with \(M\) passing through A and \(N\) passing through B .
3. Find the distance between the parallel lines \(M\) and \(N\). The point C has coordinates \(( k , 0,2 )\), and the line AC intersects the line \(N\) at the point D .
4. Find the value of \(k\), and the coordinates of D .