So, there is a plane equation $ax+by+z = 0$. Suppose there are three points $(x_1,y_1,z_1)$, $(x_2,y_2,z_2)$, $(x_3,y_3,z_3)$ that is on the given plane.
Then, $\begin{vmatrix} x & y & z & 1\\x_1 & y_1 & z_1 & 1\\x_2 & y_2 & z_2 & 1\\x_3 & y_3 & z_3 & 1 \end{vmatrix}=0$.
What happens if the three points are collinear?