 AreCoplanar - Maple Help

geom3d

 AreCoplanar
 test if the given objects are on the same plane Calling Sequence AreCoplanar(A, B, C, D) AreCoplanar(l1, l2) Parameters

 A, B, C, D - points l1, l2 - lines Description

 • 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. Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,1,1,11\right),\mathrm{point}\left(C,3,7,5\right):$
 > $\mathrm{plane}\left(p,\left[A,B,C\right]\right)$
 ${p}$ (1)

Generate a random point on p

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

Hence, A, B, C and E must be on the same plane

 > $\mathrm{AreCoplanar}\left(A,B,C,E\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{point}\left(o,0,0,0\right):$
 > $\mathrm{line}\left(\mathrm{l1},\left[o,\left[1,\frac{1}{2},\frac{1}{3}\right]\right]\right):$
 > $\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):$
 > $\mathrm{line}\left(\mathrm{l2},\left[\mathrm{p1},\mathrm{p2}\right]\right):$
 > $\mathrm{AreCoplanar}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{AreSkewLines}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (4)