Vector-valued Parametric Line

A Vector-value parametric line

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Complete Code

Download file: VectorParametricLine.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();
loadMacros(
    'PGstandard.pl',        'PGML.pl',
    'parserVectorUtils.pl', 'parserParametricLine.pl',
    'PGcourse.pl'
);

Preamble

The macro parseVectorUtils.pl provides random points. The macro parseParametricLine.pl provides the ParametricLine function which will be the answer.

Context('Vector');
Context()->variables->are(t => 'Real');

$P    = non_zero_point3D();
$disp = non_zero_vector3D();
$Q    = Point($P + $disp);
$line = ParametricLine("$P+t *$disp");

Setup

We randomize two points in three-dimensional space, P and Q, a displacement vector between them, and a speed to travel between them.

BEGIN_PGML
Find a vector parametric equation for the
line through points [` P = [$P] `] and [` Q = [$Q] `].

[` \vec{r}(t) = `] [___]{$line}

A vector should be entered like  <x(t),y(t),z(t)>.
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.