$P_1 \left( x_1, y_1, z_1 \right)$, $P_2 \left( x_2, y_2, z_2 \right)$, $P_3 \left( x_3, y_3, z_3 \right)$

$$n_x \left( x - x_1 \right) + n_y \left( y - y_1 \right) + n_z \left( z - z_1 \right) = 0 $$

$$ \begin{cases} n_x \left( x_2 - x_1 \right) + n_y \left( y_2 - y_1 \right) + n_z \left( z_2 - z_1 \right) = 0 \\ n_x \left( x_3 - x_1 \right) + n_y \left( y_3 - y_1 \right) + n_z \left( z_3 - z_1 \right) = 0 \\ n_x^2 + n_y^2 + n_z^2 = 1 \end{cases} $$