Vector-valued Parametric Line Segment (Specific)

A Vector-value parametric line segment for a specific values of the parameter.

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Complete Code

Download file: VectorLineSegment2.pg

POD for Macro Files

See Also

PG problem file

Explanation

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

Preamble

The parserVectorUtils.pl macro is loaded for the non_zero_point3D and non_zero_vector3D methods.

Context("Vector");
Context()->variables->are(t => "Real");

$P     = non_zero_point3D();
$disp  = non_zero_vector3D();
$speed = random(3, 9, 1);

$ans = Compute("$P + $speed * t * $disp / norm($disp)");

Setup

A random point is generated with the non_zero_point3D method, a random displacement vector is generated with the non_zero_vector3D method, and a random speed is generated.

Then the answer is computed from those values.

BEGIN_PGML
A particle starts at the point [`P = [$P]`] when [`t = 0`] and moves along a
straight line toward [`Q = [@ Point($P + $disp) @]`] at a speed of [`[$speed]`]
centimeters per second.  Assume that [`x`], [`y`], and [`z`] are measured in
centimeters.

Find a vector equation for the position of the object.

[` \vec{r}(t) = `] [_]{$ans}{10}

_Do not include units in your answer._
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.