1 The points \(\mathrm { A } ( 2 , - 1,3 ) , \mathrm { B } ( - 2 , - 7,7 )\) and \(\mathrm { C } ( 7,5,1 )\) are three vertices of a tetrahedron ABCD .
The plane ABD has equation \(x + 4 y + 7 z = 19\).
The plane ACD has equation \(2 x - y + 2 z = 11\).

1. Find the shortest distance from \(B\) to the plane \(A C D\).
2. Find an equation for the line AD .
3. Find the shortest distance from C to the line AD .
4. Find the shortest distance between the lines \(A D\) and \(B C\).
5. Given that the tetrahedron ABCD has volume 20, find the coordinates of the two possible positions for the vertex \(D\).