Coplanar

Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar Iff the volume of the Tetrahedron defined by them is 0,

$$\left\vert\matrix{ x_1 & y_1 & z_1 & 1\cr x_2 & y_2 & z_2 & 1\cr x_3 & y_3 & z_3 & 1\cr x_4 & y_4 & z_4 & 1\cr}\right\vert=0.$$