Collinear

Three or more points $P_1$, $P_2$, $P_3$, ..., are said to be collinear if they lie on a single straight Line $L$. (Two points are always collinear.) This will be true Iff the ratios of distances satisfy

$$x_2-x_1:y_2-y_1:z_2-z_1 = x_3-x_1:y_3-y_1:z_3-z_1.$$

Two points are trivially collinear since two points determine a Line.

See also Concyclic, Directed Angle, N-Cluster, Sylvester's Line Problem