Find the vector and Cartesian equations of the plane passing through the points $\left(2,2-1\right),\left(3,4,2\right)$ and $\left(7,0,6\right)$. Also find the vector equation of a plane passing through $\left(4,3,1\right)$ and parallel to the plane obtained above.
OR
Find the vector equation of the plane that contains the lines $\overrightarrow{\mathit{r}}=\left(\hat{\mathit{i}}+\hat{\mathit{j}}\right)+\mathit{\lambda }\left(\hat{\mathit{i}}+2\hat{\mathit{j}}-\hat{\mathit{k}}\right)$ and the point $\left(-1,3,-4\right)$. Also, find the length of the perpendicular drawn from the point $\left(2,1,4\right)$ to the plane, thus obtained.