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.\\
(i) Find the shortest distance between the lines $O C$ and $A B$.\\

(ii) Find the cartesian equation of the plane containing the line $O C$ and the common perpendicular of the lines $O C$ and $A B$.\\

\hfill \mbox{\textit{CAIE FP1 2019 Q6}}