Condition for 4 Points to be Coplanar

Theorem
Let:

be distinct points in Cartesian $3$-space.

Then $p_1$, $p_2$, $p_3$ and $p_4$ are coplanar :


 * $\begin {vmatrix} x_1 & y_1 & z_1 & 1 \\ x_2 & y_2 & z_2 & 1 \\ x_3 & y_3 & z_3 & 1 \\ x_4 & y_4 & z_4 & 1 \end {vmatrix} = 0$

where the construct is evaluated as a determinant.