Category:Three-Point Form of Equation of Plane

This category contains pages concerning the three-point form of the equation of a plane:

Let $P_1 := \tuple {x_1, y_1, z_1}$, $P_2 := \tuple {x_2, y_2, z_2}$ and $P_3 := \tuple {x_3, y_3, z_3}$ be points in a cartesian $3$-space.

Let $P$ be the plane passing through $P_1$, $P_2$ and $P_3$.

$P$ can be expressed in the form:

$\begin {vmatrix} x & y & z & 1 \\ x_1 & y_1 & z_1 & 1 \\ x_2 & y_2 & z_2 & 1 \\ x_3 & y_3 & z_3 & 1 \end {vmatrix} = 0$