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Student[MultivariateCalculus]

  

AreParallel

  

test if lines or planes are parallel

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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);

true

(1)

l3 := Line([3,2,3], <-2,6,1>):

AreParallel(l1, l3);

false

(2)

l4 := Line([0,-1,-2], <1,2,3>):

l5 := Line([-3,-2,-1], <-4,-3,2>):

AreParallel(l4, l5);

false

(3)

Intersects(l4, l5);

false

(4)

AreSkew(l4, l5);

true

(5)

l6 := Line([-1,-3], [4,5]):

l7 := Line([0,8], <5, 8>):

AreParallel(l6, l7);

true

(6)

p1 := Plane([8,2,6], <-1,-6,4>):

p2 := Plane([-2,8,-6], <1,6,-4>):

AreParallel(p1, p2);

true

(7)

p3 := Plane([3,7,1],[7,1,3],[-3,6,-10]):

AreParallel(p1, p3);

false

(8)

Compatibility

• 

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

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

Student[MultivariateCalculus]

Student[MultivariateCalculus][Line]

Student[MultivariateCalculus][Plane]

Student[MultivariateCalculus][Equal]

Student[MultivariateCalculus][Contains]

Student[MultivariateCalculus][Intersects]