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geom3d[line] - define a line
Calling Sequence
line(l, [A, B] )
line(l, [A, v] )
line(l, [A, dseg] )
line(l, [A, p1] )
line(l, [p1, p2] )
line(l, [, , ], t)
Parameters
l
-
the name of the line
A, B
points
v
vector
dseg
directed line segment
p1, p2
planes
a1, a2, a3, b1, b2, b3
algebraic expressions
t
(optional) a name denoting the parameter in the parametric equations of the line.
Description
A line l can be defined as follows:
+ from two given points A and B
+ from a given point A and a vector v of dimension 3 or a directed segment seg. The line defined is the line that passes through A and has v as its direction-ratios.
+ from a given point A and a plane p1. The line defined is the line that passes through A and perpendicular to the plane p1.
+ from two given planes p1 and p2. The line defined is the line of intersection of two planes p1 and p2 (if exists).
+ from the parametric equations of the line . If the third optional argument t is not given, and if a name is assigned to the environment variable _EnvTName, then this name will be used as the name of the parameter in the parametric equations of the line. Otherwise, Maple will prompt the user to input the name of the parameter.
To access the information relating to a line l, use the following function calls:
form(l)
returns the form of the geometric object
(i.e., line3d if l is a line).
FixedPoint(l)
returns a fixed point on l.
ParallelVector(l)
returns a direction-ratios of l.
DirectionRatios(l)
returns the direction-ratios of l.
Equation(l)
returns the parametric equations
that represents the line l.
xname(l), yname(l), or zname(l)
returns the name of
the x-axis; y-axis, z-axis or FAIL if
the axis is not assigned to any name.
detail(l)
returns a detailed description of
the line l.
The command with(geom3d,line) allows the use of the abbreviated form of this command.
Examples
Find the equation of the line through [1,2,-1] perpendicular to the plane 3*x-5*y+4*z=5,the length of the perpendicular, and the coordinates of its foot
the parametric equations of the line l with parameter t is
the projection of A on the plane is
the length of the perpendicular is
Let the straight line pass through the point A=[x1,y1,z1] and has direction-cosines (or ratios) [l,m,n]
define the line l1 that passes through A and has [l,m,n] as its direction-ratios
Warning, assume that the parameter in the parametric equations is _t Warning, assuming that the names of the axes are _x, _y, and _z
define the line l which is the intersection of two given planes p1, p2
See Also
geom3d[altitude], geom3d[intersection], geom3d[objects], geom3d[transformation]
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