Vector-valued Parametric Line

A Vector-value parametric line

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Complete Code

Download file: VectorParametricLine.pg

POD for Macro Files

See Also

PG problem file

Explanation

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

Preamble

The parserVectorUtils.pl macro provides the non_zero_point3D and non_zero_vector3D methods. The macro parserParametricLine.pl provides the ParametricLine function used for the answer.

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

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

Setup

Generate a random three dimensional initial point $P using the non_zero_point3D method, and a random three dimensional displacement vector $disp using the non_zero_vector3D method. Use the ParametricLine method to create the answer which is the parametric line through $P in the direction of $disp.

BEGIN_PGML
Find a vector parametric equation for the line through points [`P = [$P]`] and
[`Q = [@ Point($P + $disp) @]`].

[`\vec{r}(t) =`] [_]{$line}{15}

Give A vector in the form  [|<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.