View source for VectorParametricLines1

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<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Parametric/VectorParametricLines.html a newer version of this problem]</p>

<h2>Vector Parametric Lines</h2>

[[File:VectorParametricLines1.png|300px|thumb|right|Click to enlarge]]
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This PG code shows how to require students to enter a parametrized line that must go through certain points when t=0 and t=1, or allow them to enter an equation for any parametric line through two points.
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* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Parametric/VectorParametricLines1.pg FortLewis/Authoring/Templates/Parametric/VectorParametricLines1.pg]
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Parametric/VectorParametricLines1_PGML.pg FortLewis/Authoring/Templates/Parametric/VectorParametricLines1_PGML.pg]

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<th> PG problem file </th>
<th> Explanation </th>
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[http://webwork.maa.org/wiki/Tagging_Problems Problem tagging data]
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<b>Problem tagging:</b>
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<pre>
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"parserParametricLine.pl",
);

TEXT(beginproblem());
</pre>
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<p>
<b>Initialization:</b>
We load <code>parserVectorUtils.pl</code> which provides the <code>Line()</code> subroutine for a particular parametrization of a line, as well as <code>parserParametricLine.pl</code> which provides a subroutine <code>ParametricLine()</code> that allows students to enter any parametrization.
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<pre>
Context("Vector")->variables->are(t=>"Real");

$P = non_zero_point3D(-9,9,1);
$V = non_zero_vector3D(-9,9,1);

$Q = Point($P + $V);

$particular = Line($P,$V,'t');
$general = ParametricLine($P,$V);
</pre>
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<p>
<b>Setup:</b> 
For the answer which is a particular parametrization through two points at times t=0 and t=1, we use <code>Line()</code>.  To allow students to enter any equation for a parametric line through two points, we use <code>ParametricLine()</code>  The syntax is fairly self-explanatory.
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<pre>
Context()->texStrings;
BEGIN_TEXT
(a) Find a vector parametric equation for the 
line that goes through the point \( $P \) 
when \( t = 0 \) and the point \( $Q \) when
\( t = 1 \).
$BR
\( \vec{L}(t) = \)
\{ ans_rule(30) \}
$BR
$BR
(b) Find any vector parametric equation for the 
line that goes through the points \( $P \) and 
\( $Q \).
$BR
\( \vec{L}(t) = \)
\{ ans_rule(30) \}
END_TEXT
Context()->normalStrings;
</pre>
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<b>Main Text:</b>
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<pre>
$showPartialCorrectAnswers = 1;

ANS( $particular->cmp() );
ANS( $general->cmp() );
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<b>Answer Evaluation:</b>
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<pre>
Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();
</pre>
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<b>Solution:</b>
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