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Student[MultivariateCalculus][GetRepresentation] - obtain a representation of a line or plane

Calling Sequence

GetRepresentation(l, opts)

GetRepresentation(p, opts)

Parameters

l

-

Line ; Line defined by Student[MultivariateCalculus]

opts

-

(optional) control the representation of a Line object

p

-

Plane ; Plane defined by Student[MultivariateCalculus]

Description

• 

The GetRepresentation command returns a representation of a line or plane.

• 

For a Plane object p, the command returns the equation of p in the form ax+by+cz=d.

• 

For consistency with lines in 3D (see below), one can pass the option form = equations (plural) to GetRepresentation to get this equation in a set. The only other valid value for form is equation (singular), which is the default - it returns just the equation.

• 

For a Line object l, several forms of representation are available. These are selected by the form option (see below).

• 

When form = symmetric is selected for a typical line in 3D space (see the options below), the result is not a normal Maple equation - Maple does not support equations involving three expressions. The value returned can only be used for displaying this 'equation'. The other forms all result in normal Maple equations and expressions.

Examples

withStudent:-MultivariateCalculus:

l1:=Line1,2,3,7,2,1,'variables'=u,v,w

l1:=<< Line 1 >>

(1)

GetRepresentationl1

t&period;644&plus;123

(2)

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;vectors&apos;&comma;&apos;parameter&apos;&equals;&apos;k&apos;

k&period;644&plus;123

(3)

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;combined_vector&apos;

1&plus;6t24t34t

(4)

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;parametric&apos;

u&equals;1&plus;6t&comma;v&equals;24t&comma;w&equals;34t

(5)

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;symmetric&apos;

u616 = v4+12 = w4+34

(6)

The other symmetric forms.

l2:=Line1&comma;2&comma;3&comma;7&comma;2&comma;3&comma;&apos;variables&apos;&equals;u&comma;v&comma;w

l2:=<< Line 2 >>

(7)

GetRepresentationl2&comma;&apos;form&apos;&equals;&apos;symmetric&apos;

16u16&equals;14v&plus;12&comma;w&equals;3

(8)

l3:=Line1&comma;2&comma;3&comma;7&comma;2&comma;3&comma;&apos;variables&apos;&equals;u&comma;v&comma;w

l3:=<< Line 3 >>

(9)

GetRepresentationl3&comma;&apos;form&apos;&equals;&apos;symmetric&apos;

v&equals;2&comma;w&equals;3

(10)

l4:=Line1&comma;2&comma;7&comma;2&comma;&apos;variables&apos;&equals;u&comma;v

l4:=<< Line 4 >>

(11)

GetRepresentationl4&comma;&apos;form&apos;&equals;&apos;symmetric&apos;

16u16&equals;14v&plus;12

(12)

l5:=Line1&comma;2&comma;7&comma;2&comma;&apos;variables&apos;&equals;u&comma;v

l5:=<< Line 5 >>

(13)

GetRepresentationl5&comma;&apos;form&apos;&equals;&apos;symmetric&apos;

v&equals;2

(14)

The option form&equals;equation is available for lines in 2D, but not 3D.

GetRepresentationl4&comma;&apos;form&apos;&equals;&apos;equation&apos;

23u&plus;v&equals;83

(15)

GetRepresentationl4&comma;&apos;form&apos;&equals;&apos;equations&apos;

23u&plus;v&equals;83

(16)

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;equation&apos;

Error, (in Student:-MultivariateCalculus:-Line:-GetRepresentation) a line in 3 dimensions cannot be given by a single equation; try 'form = equations' instead

GetRepresentationl1&comma;&apos;form&apos;&equals;&apos;equations&apos;

23u&plus;v&equals;83&comma;23u&plus;w&equals;113

(17)

p1:=Plane2&comma;3&comma;3&comma;0&comma;3&comma;1&colon;

GetRepresentationp1

3y&plus;z&equals;6

(18)

p2:=Plane9&comma;4&comma;3&comma;9&comma;1&comma;3&comma;1&comma;0&comma;0

p2:=<< Plane 2 >>

(19)

GetRepresentationp2

3yz&equals;15

(20)

u, v and x can be used in the equation.

p3:=Plane3&comma;6&comma;1&comma;4&comma;1&comma;5&comma;3&comma;2&comma;0&comma;&apos;variables&apos;&equals;u&comma;v&comma;x&colon;

GetRepresentationp3

19u&plus;v4x&equals;55

(21)

See Also

Student[MultivariateCalculus], Student[MultivariateCalculus][Line]


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