Vector Equation of Plane

In $R^3$, a plane $\vec{r}$ is determined by a vector $\vec{r}=[x_0,y_0,z_0]$ and 2 non-collinear vectors $\vec{a}=[a_1,a_2,a_3]$ and $\vec{b}=[b_1,b_2,b_3]$ $\vec{r}=\overrightarrow{r_0}+s\vec{a}+t\vec{b}$ You need 2 direction vectors for a plane

In terms of vectors created by points A,B,C, $\vec{r}=A+s(\overrightarrow{AB})+t(\overrightarrow{AC})$