ImplicitPlane: Difference between revisions

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<h2>Planes Defined Implicitly</h2>
<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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$B = Point($A + $AB);
$B = Point($A + $AB);
$C = Point($A + $AC);
$C = Point($A + $AC);
$answer = ImplicitPlane($A,$N);
</pre>
</pre>
</td>
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<b>Setup:</b>  
<b>Setup:</b>  
Create points and vectors.  Make sure that the vectors are not parallel.
Create points and vectors.  Make sure that the vectors are not parallel.
</p>
<p>
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.
<pre>
Context("ImplicitPlane");
Context()->variables->are(x=>"Real",y=>"Real");
$answer = ImplicitPlane("y=4x+3");
</pre>
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Context()->texStrings;
Context()->texStrings;
BEGIN_TEXT
BEGIN_TEXT
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)\}.
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>
ANS(ImplicitPlane($A,$N)->cmp);
ANS( $answer->cmp );
$showPartialCorrectAnswers = 1;
$showPartialCorrectAnswers = 1;


Revision as of 00:36, 7 February 2010

Planes or Lines Defined Implicitly

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

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.

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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