6 The points \(A , B , C\) have position vectors $$\mathbf { i } + \mathbf { j } , \quad - \mathbf { i } + 2 \mathbf { j } + 4 \mathbf { k } , \quad - 2 \mathbf { i } + \mathbf { j } + 3 \mathbf { k } ,$$ respectively, relative to the origin \(O\).

1. Find the equation of the plane \(A B C\), giving your answer in the form \(a x + b y + c z = d\).
2. Find the perpendicular distance from \(O\) to the plane \(A B C\).
3. Find a vector equation of the common perpendicular to the lines \(O C\) and \(A B\).