Parametric Equation of Plane

position vector: $\vec{r}=[x_0,y_0,z_0]$ 2 non-collinear direction vectors $\vec{a}=[a_1,a_2,a_3]$ and $\vec{b}=[b_1,b_2,b_3]$ $x=x_0+s{a}_1+t{b}_1$ $y=y_0+s{a}_2+t{b}_2$ $x=x_0+s{a}_3+t{b}_3$