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Student[MultivariateCalculus]

 AreParallel
 test if lines or planes are parallel

 Calling Sequence AreParallel(l1, l2) AreParallel(p1, p2) AreParallel(l1, p1) AreParallel(p1, l1)

Parameters

 l1, l2 - Line; Line defined in Student[MultivariateCalculus] p1, p2 - Plane; Plane defined in Student[MultivariateCalculus]

Description

 • The AreParallel command determines if two lines or two planes are parallel or not, or if a line and a plane are parallel.
 • The Line can be either in 2D or 3D.
 • Two Line objects in 3D can be non-intersecting but not parallel to each other.  This property between such lines, which is called skewness, can be detected using AreSkew.
 • Two identical lines or two identical planes are parallel to each other. Similarly, a line that lies in a plane is parallel to that plane.

Examples

 > with(Student[MultivariateCalculus]):
 > l1 := Line([0,2,6], <10,15,20>):
 > l2 := Line([-3,7,3], <2,3,4>):
 > AreParallel(l1,l2);
 ${\mathrm{true}}$ (1)
 > l3 := Line([3,2,3], <-2,6,1>):
 > AreParallel(l1, l3);
 ${\mathrm{false}}$ (2)
 > l4 := Line([0,-1,-2], <1,2,3>):
 > l5 := Line([-3,-2,-1], <-4,-3,2>):
 > AreParallel(l4, l5);
 ${\mathrm{false}}$ (3)
 > Intersects(l4, l5);
 ${\mathrm{false}}$ (4)
 > AreSkew(l4, l5);
 ${\mathrm{true}}$ (5)
 > l6 := Line([-1,-3], [4,5]):
 > l7 := Line([0,8], <5, 8>):
 > AreParallel(l6, l7);
 ${\mathrm{true}}$ (6)
 > p1 := Plane([8,2,6], <-1,-6,4>):
 > p2 := Plane([-2,8,-6], <1,6,-4>):
 > AreParallel(p1, p2);
 ${\mathrm{true}}$ (7)
 > p3 := Plane([3,7,1],[7,1,3],[-3,6,-10]):
 > AreParallel(p1, p3);
 ${\mathrm{false}}$ (8)

Compatibility

 • The Student[MultivariateCalculus][AreParallel] command was introduced in Maple 17.