6 With \(O\) as the origin, the points \(A , B , C\) have position vectors
$$\mathbf { i } - \mathbf { j } , \quad 2 \mathbf { i } + \mathbf { j } + 7 \mathbf { k } , \quad \mathbf { i } - \mathbf { j } + \mathbf { k }$$
respectively.
- Find the shortest distance between the lines \(O C\) and \(A B\).
- Find the cartesian equation of the plane containing the line \(O C\) and the common perpendicular of the lines \(O C\) and \(A B\).