The routine returns true if the four given points or two given lines are coplanar (i.e., they are on the same plane); false if they are not; and FAIL if it is unable to reach a conclusion.

The command with(geom3d,AreCoplanar) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{point}\left(A\,0\,0\,0\right),\mathrm{point}\left(B\,1\,1\,11\right),\mathrm{point}\left(C\,3\,7\,5\right)\:$

$\mathrm{plane}\left(p\,\left[A\,B\,C\right]\right)$

$p$

$\mathrm{randpoint}\left(E\,p\right)\:$

$\mathrm{AreCoplanar}\left(A\,B\,C\,E\right)$

$\mathrm{true}$

$\mathrm{point}\left(o\,0\,0\,0\right)\:$

$\mathrm{line}\left(\mathrm{l1}\,\left[o\,\left[1\,\frac{1}{2}\,\frac{1}{3}\right]\right]\right)\:$

$\mathrm{plane}\left(\mathrm{p1}\,3x-4y+5z=10\,\left[x\,y\,z\right]\right)\:$$\mathrm{plane}\left(\mathrm{p2}\,2x+2y-3z=4\,\left[x\,y\,z\right]\right)\:$

$\mathrm{line}\left(\mathrm{l2}\,\left[\mathrm{p1}\,\mathrm{p2}\right]\right)\:$

$\mathrm{AreCoplanar}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\mathrm{false}$

$\mathrm{AreSkewLines}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\mathrm{true}$