|\^/|     Maple V Release 3 (SUNY at Albany)
._|\|   |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
 \  MAPLE  /  University of Waterloo. All rights reserved. Maple and Maple V
 <____ ____>  are registered trademarks of Waterloo Maple Software.
      |       Type ? for help.


# A line is determined by a direction vector <b>v</b> and a position vector <b>u</b>.

> with(linalg):

Warning: new definition for   norm
Warning: new definition for   trace

> v := vector(3); u := vector(3);

                             v := array(1 .. 3, [])

                             u := array(1 .. 3, [])

# Yes, this is the way in which maple tells that <b>v</b> and <b>u</b>
are two arbitrary vectors in 3 dimensional space.
<p> The equation of the line with direction <b>v</b> and passing through <b>u</b> is:

> Line := { u + t*v};

                               Line := {u + t v}

# This is the set of all the vectors of the form:<br>
 "position vector + a scalar multiple of the direction vector". The scalar "t"
 is a parameter that can take any value from -infinity to infinity. The
 position vector of every point on the line can be written as a function
 of the parameter "t" as follows:

> L := t -> u + t*v;

                               L := t -> u + t v

> L(0);

                                       u

> L(1);

                                     u + v

# To see the coordinates of L(t) in the standard basis, just evalm:

> evalm(L(t));

                [ u[1] + t v[1], u[2] + t v[2], u[3] + t v[3] ]

# The vector L(t) can be interpreted as the position at time "t"
of a particle moving with constant velocity vector <b>v</b> that
is found at position <b>u</b> at an innitial time 0. The following
two commands will display a picture of the line with velocity vector
[1,-2,,3] and position vector [2,1,-1].

> with(plots);

 [animate, animate3d, conformal, contourplot, cylinderplot, densityplot,

     display, display3d, fieldplot, fieldplot3d, gradplot, gradplot3d,

     implicitplot, implicitplot3d, loglogplot, logplot, matrixplot, odeplot,

     pointplot, polarplot, polygonplot, polygonplot3d, polyhedraplot, replot,

     setoptions, setoptions3d, spacecurve, sparsematrixplot, sphereplot,

     surfdata, textplot, textplot3d, tubeplot]

# Notice that the next command "spacecurve" was loaded with the "with" above.


! wlot(`lines-planes-maple1.gif`,spacecurve,[2+t, 1-2*t, -1+3*t], t=-4..4, axes=NORMAL, color=RED);


>