Points, planes and a line parallel to a plane

Show that the points $A$, $B$ and $C$ do not lie on a straight line.

Find the Cartesian equation of the plane $P$.

Now consider the plane $Q$, given by $2x - y + 3z = 1$, and the line $L$, given by $\tvec{r}(t) = \tvec{i} - 2\tvec{j} + 3\tvec{k} + t\left(2\tvec{i} + \tvec{j} - \tvec{k}\right)$, $t \in \R$.

Show that the line $L$ does not intersect the plane $Q$.

Find the shortest distance from the line $L$ to the plane $Q$.