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Student[MultivariateCalculus][GetIntersection] - obtain the intersection of lines or planes

Calling Sequence

GetIntersection(pl1, pl2)

Parameters

pl1, pl2

-

list, Line, Plane ; points or Line or Plane objects defined by Student[MultivariateCalculus].

Returns

• 

the empty set, , if the lines or planes don't intersect.

• 

a list of coordinate values, if the intersection is a point.

• 

a Line or Plane object, if that is the intersection.

Description

• 

The GetIntersection command obtains the intersection of two point, Line, or Plane objects as understood by the Student[MultivariateCalculus] package.

• 

The Intersects command can be used to test if lines and/or planes intersect.

• 

The empty set, denoted by , is returned if the lines or planes do not intersect.

• 

If one object is contained in another, then their intersection is the smaller object. In particular, the intersection of any object A with itself is that object A.

Examples

withStudent[MultivariateCalculus]:

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

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

AreParallell1,l2

true

(1)

Intersectsl1,l2

false

(2)

GetIntersectionl1,l2

(3)

p1:=Plane0,3,1,0,3,2:

p2:=Plane4,1,3,0,3,2:

Intersectsp1,p2

false

(4)

GetIntersectionp1,p2

(5)

Intersectsp1,l2

true

(6)

GetIntersectionp1,l2

8317,7117,1317

(7)

Intersectsl1,p2

true

(8)

GetIntersectionp2,l1

1817,717,6617

(9)

p3:=Plane0,0,0,3,3,1:

Intersectsp1,p3

true

(10)

l3:=GetIntersectionp1,p3:

GetDirectionl3

369

(11)

GetPointl3

12142,4421,3314

(12)

See Also

Student[MultivariateCalculus], Student[MultivariateCalculus][Line], Student[MultivariateCalculus][Plane], Student[MultivariateCalculus][AreParallel], Student[MultivariateCalculus][AreSkew], Student[MultivariateCalculus][Contains], Student[MultivariateCalculus][Intersects]


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