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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

withStudent[MultivariateCalculus]:

l1Line0,2,6,10,15,20:

l2Line3,7,3,2,3,4:

AreParallell1,l2

true

(1)

l3Line3,2,3,2,6,1:

AreParallell1,l3

false

(2)

l4Line0,1,2,1,2,3:

l5Line3,2,1,4,3,2:

AreParallell4,l5

false

(3)

Intersectsl4,l5

false

(4)

AreSkewl4,l5

true

(5)

l6Line1,3,4,5:

l7Line0,8,5,8:

AreParallell6,l7

true

(6)

p1Plane8,2,6,1,6,4:

p2Plane2,8,6,1,6,4:

AreParallelp1,p2

true

(7)

p3Plane3,7,1,7,1,3,3,6,10:

AreParallelp1,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]

 


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