AreCollinear - Maple Help
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geom3d

 AreCollinear
 test if three points are collinear

 Calling Sequence AreCollinear(P, Q, R, cond)

Parameters

 P, Q, R - three points cond - (optional) name

Description

 • Points P, Q, R are said to be collinear if they lie on the same straight line.
 • The routine returns true if P, Q, and R are collinear; false if they are not; and FAIL in case it is unable to determine if the three points are collinear.
 • If FAIL is returned, and the optional argument cond is given, the condition that makes the points collinear is assigned to this argument.
 • The command with(geom3d,AreCollinear) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,1,0,0\right),\mathrm{point}\left(C,11,0,0\right):$
 > $\mathrm{AreCollinear}\left(A,B,C\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{point}\left(C,a,b,c\right):$
 > $\mathrm{AreCollinear}\left(A,B,C,'\mathrm{cond}'\right)$
 ${\mathrm{FAIL}}$ (2)

make necessary assumption so that A, B, C are collinear

 > $\mathrm{assume}\left(\mathrm{op}\left(\mathrm{cond}\right)\right)$
 > $\mathrm{AreCollinear}\left(A,B,C\right)$
 ${\mathrm{true}}$ (3)