Normal and parametric equations for a plane in the 3D space

Given $r_0$ is in the plane, then any other point in the plane should be equal to $r_0$ plus a directional vector. This directional vector is a linear combination of two base vectors $v_1, v_2$:

$$\vec{r} = \vec{r_0} + s\vec{v_1} + t\vec{v_2}$$

The above equation is parametric, with the parameters being $s, t$. The plane can also be expressed in terms of the normal vector (orthogonal to the plane):

$$\vec{n} = \vec{v_1} \times t\vec{v_2}$$

and:

$$\vec{n} \cdot \vec{r} = \vec{n} \cdot \vec{r_0}$$