Difference between revisions of "ImplicitPlane"

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<h2>Planes Defined Implicitly</h2>
  
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{{historical}}
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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problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/DiffCalcMV/ImplicitPlane.html a newer version of this problem]</p>
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<h2>Planes or Lines Defined Implicitly</h2>
   
 
<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
  
<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
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<em>This shows the PG code to evaluate answers that are planes defined implicitly by an equation.</em>
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<em>This shows the PG code to evaluate answers that are planes or lines defined implicitly by an equation.
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<br />
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<br />
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You may also be interested in [http://webwork.maa.org/wiki/EquationsDefiningFunctions EquationsDefiningFunctions]</em>
 
</p>
  
</p>
   
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[[IndexOfProblemTechniques|Problem Techniques Index]]
  
[[IndexOfProblemTechniques|Problem Techniques Index]]
 
</p>
  
</p>
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<table cellspacing="0" cellpadding="2" border="0">
  
<table cellspacing="0" cellpadding="2" border="0">
 
<tr valign="top">
  
<tr valign="top">
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loadMacros(
  
loadMacros(
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"PGstandard.pl",
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"PGstandard.pl",
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"MathObjects.pl",
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"parserImplicitPlane.pl",
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"parserImplicitPlane.pl",
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"parserVectorUtils.pl",
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"parserVectorUtils.pl",
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"PGcourse.pl",
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"PGcourse.pl",
  
 
);
  
);
   
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TEXT(beginproblem);
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TEXT(beginproblem());
 
</pre>
  
</pre>
 
</td>
  
</td>
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<p>
  
<p>
 
<b>Initialization:</b>
 
<b>Initialization:</b>
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In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file.
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In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file, which automatically loads <code>MathObjects.pl</code>.
 
</p>
  
</p>
 
</td>
  
</td>
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$B = Point($A + $AB);
  
$B = Point($A + $AB);
 
$C = Point($A + $AC);
  
$C = Point($A + $AC);
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  +
$answer = ImplicitPlane($A,$N);
 
</pre>
  
</pre>
 
</td>
  
</td>
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<p>
  
<p>
 
<b>Setup:</b>
 
<b>Setup:</b>
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Create points and vectors. Make sure that the vectors are not parallel.
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Create points and vectors. Make sure that the vectors are not parallel. There are several other ways to define planes implicitly, which are explained at
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[http://webwork.maa.org/pod/pg/macros/parserImplicitPlane.html parserImplicitPlane.pl]
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</p>
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<p>
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If the correct answer is a line in 2D space instead of a plane in 3D space, the only modification needed is to reduce the number of variables to two, which will modify error messages accordingly.
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<pre>
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Context("ImplicitPlane");
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Context()->variables->are(x=>"Real",y=>"Real");
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$answer = ImplicitPlane("y=4x+3");
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</pre>
 
</p>
  
</p>
 
</td>
  
</td>
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Context()->texStrings;
  
Context()->texStrings;
 
BEGIN_TEXT
  
BEGIN_TEXT
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An implicit equation for the plane passing through the points
  
An implicit equation for the plane passing through the points
 
\($A\), \($B\), and \($C\) is \{ans_rule(40)\}.
  
\($A\), \($B\), and \($C\) is \{ans_rule(40)\}.
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END_TEXT
  
END_TEXT
 
Context()->normalStrings;
  
Context()->normalStrings;
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<td style="background-color:#eeddff;border:black 1px dashed;">
  
<td style="background-color:#eeddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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ANS(ImplicitPlane($A,$N)->cmp);
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ANS( $answer->cmp );
 
$showPartialCorrectAnswers = 1;
  
$showPartialCorrectAnswers = 1;
   
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[[IndexOfProblemTechniques|Problem Techniques Index]]
  
[[IndexOfProblemTechniques|Problem Techniques Index]]
 
</p>
  
</p>
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  +
  +
  +
<ul>
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<li>POD documentation: [http://webwork.maa.org/pod/pg/macros/parserImplicitPlane.html parserImplicitPlane.pl]</li>
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<li>PG macro code: [http://webwork.maa.org/viewvc/system/trunk/pg/macros/parserImplicitPlane.pl?view=log parserImplicitPlane.pl]</li>
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</ul>
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  +
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<ul>
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<li>POD documentation: [http://webwork.maa.org/pod/pg/macros/parserVectorUtils.html parserVectorUtils.pl]</li>
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<li>PG macro code: [http://webwork.maa.org/viewvc/system/trunk/pg/macros/parserVectorUtils.pl?view=log parserVectorUtils.pl]</li>
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</ul>
   
 
[[Category:Problem Techniques]]
  
[[Category:Problem Techniques]]

Latest revision as of 11:12, 16 July 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem


Planes or Lines Defined Implicitly

This shows the PG code to evaluate answers that are planes or lines defined implicitly by an equation.

You may also be interested in EquationsDefiningFunctions

Problem Techniques Index

PG problem file Explanation 
DOCUMENT(); 

loadMacros(
"PGstandard.pl",
"parserImplicitPlane.pl",
"parserVectorUtils.pl",
"PGcourse.pl",
);

TEXT(beginproblem());

Initialization: In particular, we need to include the parserImplicitPlane.pl macro file, which automatically loads MathObjects.pl. 

Context("ImplicitPlane");
#  Vectors in the plane
$AB = non_zero_vector3D();
$AC = non_zero_vector3D(); 
while (areParallel $AB $AC) {$AC = non_zero_vector3D()}

#  The normal vector
$N = cross $AB $AC; # or $N = $AB x $AC;
#  The points A, B and C
$A = non_zero_point3D();
$B = Point($A + $AB);
$C = Point($A + $AC);

$answer = ImplicitPlane($A,$N);

Setup: Create points and vectors. Make sure that the vectors are not parallel. There are several other ways to define planes implicitly, which are explained at parserImplicitPlane.pl

If the correct answer is a line in 2D space instead of a plane in 3D space, the only modification needed is to reduce the number of variables to two, which will modify error messages accordingly. 

Context("ImplicitPlane");
Context()->variables->are(x=>"Real",y=>"Real");

$answer = ImplicitPlane("y=4x+3");


Context()->texStrings;
BEGIN_TEXT
An implicit equation for the plane passing through the points
\($A\), \($B\), and \($C\) is \{ans_rule(40)\}.
END_TEXT
Context()->normalStrings;

Main Text: Self-explanatory. 

ANS( $answer->cmp );
$showPartialCorrectAnswers = 1;

ENDDOCUMENT();

Answer Evaluation: Just specify a point $A and a normal vector $N.

Problem Techniques Index



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