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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

withStudent[MultivariateCalculus]:

l1:=Line0,2,6,10,15,20:

l2:=Line3,7,3,2,3,4:

AreParallell1,l2

true

(1)

l3:=Line3,2,3,2,6,1:

AreParallell1,l3

false

(2)

l4:=Line0,1,2,1,2,3:

l5:=Line3,2,1,4,3,2:

AreParallell4,l5

false

(3)

Intersectsl4,l5

false

(4)

AreSkewl4,l5

true

(5)

l6:=Line1,3,4,5:

l7:=Line0,8,5,8:

AreParallell6,l7

true

(6)

p1:=Plane8,2,6,1,6,4:

p2:=Plane2,8,6,1,6,4:

AreParallelp1,p2

true

(7)

p3:=Plane3,7,1,7,1,3,3,6,10:

AreParallelp1,p3

false

(8)

See Also

Student[MultivariateCalculus], Student[MultivariateCalculus][Line], Student[MultivariateCalculus][Plane], Student[MultivariateCalculus][Equal], Student[MultivariateCalculus][Contains] Student[MultivariateCalculus][Intersects]


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