Parametric equations of a plane
Determine the parametric equation of a plane that goes through point $A = (1, 0, 3)$ and has as director vectors $\overrightarrow{u}= (-1, 3, 2)$ and $\overrightarrow{v}= (2, 1, 0)$.
Component by component we obtain the parametric equations: $$\left\{\begin{array}{l} x=1-k+2m \\ y=3k+m \\ z=3+2k \end{array}\right.$$
$\left\{\begin{array}{l} x=1-k+2m \\ y=3k+m \\ z=3+2k \end{array}\right.$