Find an equation of the plane that contains the origin and is parallel to the line with parametric equations x=4+2t, y=3-t,z=-2+t and to the line with vector equation r(t)=(4,2,1)+t(1,-2,3).
The normal vector for the plane is $\displaystyle \left| {\begin{array}{rrr} i & j & k \\
2 & { - 1} & 1 \\
1 & { - 2} & 3 \\
\end{array}} \right| = - i - 5j - 3k$.
Now you write the equation of the plane with thise normal that contains the point (0,0,0).