Student[MultivariateCalculus][Line]  Create and initialize a line object

Calling Sequence


Line(eqn, opts)
Line(expr, opts)
Line(eqn1, eqn2, opts)
Line(expr1, expr2, opts)
Line(vt, opts)
Line(eqnlst, opts)
Line(exprlst, opts)
Line(p1, v, opts)
Line(v, pt, opts)
Line(p1, p2, opts)
Line(p1, P1, opts)
Line(P1, p1, opts)
Line(P1, P2, opts)
Line(ln, opts)


Parameters


eqn



Linear equation of a line in 2D

expr



Linear expression, equated to 0 to get a line in 2D

eqn1, eqn2



Equations of two intersecting planes

expr1, expr2



Expressions which, when equated to 0, define two intersecting planes

vt



Vector defining a generic point on the line parametrically

eqnlst



List of parametric equations, defining a generic point on the line

exprlst



List of parametric expressions, defining a generic point on the line

p1, p2



Points on the line, specified as lists of coordinates

v



Direction Vector of the line

P1, P2



Plane defined by Student[MultivariateCalculus]

ln



Existing Line object

opts



(optional) equations controlling the representation or the plot of the line





Options


•

The opts arguments can contain one or more of the following options.


The variable name used in the parametric form. This is used in interpreting the parametric forms of the call to the Line function, when obtaining the parametric form of the line using the GetRepresentation command, and with eval as explained above. The default is .


The variables to be used in the line's equation. This is used in interpreting the equation and expression forms of the call to the Line function, and when obtaining equations for the line. The default is .

•

id = positive integer, name, or string


Lines display as , where is an identification for the line that is by default a positive integer assigned in order of creation. The id option can be used to force the line to be given a different identification. It is an error to use the same identification for two different lines that are both in use.



Description


•

The Line command creates a line object that can be operated on or graphed. The line can be in two or threedimensional space.

•

Lines can be specified in the following ways:

–

A linear equation eqn, such as , defining a line in twodimensional space.

–

An expression expr of the form , which is set equal to 0 to obtain a line in twodimensional space.

–

Two linear equations, eqn1 and eqn2, such as , which together define a line in threedimensional space.

–

Two linear expressions, expr1 and expr2, such as , which are set equal to 0 to obtain a line in threedimensional space.

–

A Vector vt specifying the line in parametric form, such as or .

–

A list eqnlst of parametric equations, such as .

–

A list exprlst of parametric equations, such as .

–

A point p1, such as , and a nonzero Vector v, such as , giving a point on the line and the direction of the line, respectively. The point and direction can also be specified in the other order.

–

Two different points p1 and p2 on the line, such as and .

–

A point p1, such as , and a Plane object P1 defined earlier, such as . The line this defines is the one that contains p1 and is normal to P1. The point and plane can also be specified in the other order.

–

Two intersecting Plane objects P1 and P2 defined earlier, such as and . The line this defines is the intersection between P1 and P2.

–

A line ln defined earlier, such as . (This can be useful to change the names of the coordinate variables and the parameter, using the options explained below.)

•

It is possible to specify two mathematically identical lines using different Line commands.

•

The following is a list of commands available to Line objects:



Compatibility


•

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



Examples


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Lines in 2D
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 (1) 
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 (3) 
Note how lines and are displayed using their automatically assigned identification, but has the explicitly specified identification l3:
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 (4) 
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 (6) 
Lines in 3D
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Some previously defined lines in other standard forms.
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 (14) 
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 (16) 
eval can be used for substituting the unknowns and the free variable of the vector form.
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 (20) 
Query the properties of individual lines.
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 (25) 
Determine the relationship between two lines.
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 (26) 
These two lines have no intersection.
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 (27) 
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 (31) 
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 (32) 

