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geom3d

 AreParallel
 test if two objects are parallel to each other

 Calling Sequence AreParallel(dseg1, dseg2, cond) AreParallel(l1, l2, cond) AreParallel(l1, p1, cond) AreParallel(p1, p2, cond)

Parameters

 dseg1, dseg2 - directed line segments l1, l2 - lines p1, p2 - planes cond - (optional) a name

Description

 • The routine returns true if the two given objects are parallel to each other; false if they are not; and FAIL if it is unable to reach a conclusion.
 • In case of FAIL, if the third optional argument is given, the condition that makes them parallel to each other is assigned to this argument.
 • The command with(geom3d,AreParallel) allows the use of the abbreviated form of this command.

Examples

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

To view the results of the following example, copy and paste the commands and execute. Define two planes pp1, pp2

 > $\mathrm{assume}\left(\mathrm{l1}\ne 0,\mathrm{l2}\ne 0,\mathrm{l1}\ne \mathrm{l2},t\ne 0\right)$
 > $\mathrm{plane}\left(\mathrm{pp1},\mathrm{l1}x+\mathrm{p1}y+\mathrm{n1}z+\mathrm{p1},\left[x,y,z\right]\right)$
 > $\mathrm{plane}\left(\mathrm{pp2},\mathrm{l2}x+\mathrm{p2}y+\mathrm{n2}z+\mathrm{p2},\left[x,y,z\right]\right)$

Find the condition that makes pp1 and pp2 parallel to each other

 > $\mathrm{AreParallel}\left(\mathrm{pp1},\mathrm{pp2},'\mathrm{cond}'\right)$
 > $\mathrm{additionally}\left(\mathrm{op}\left(\mathrm{cond}\right)\right)$
 > $\mathrm{AreParallel}\left(\mathrm{pp1},\mathrm{pp2}\right)$