ImplicitPlane: Difference between revisions
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<h2>Planes Defined Implicitly | <h2>Planes 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;"> | ||
<em>This | <em>This shows the PG code to evaluate answers that are planes defined implicitly by an equation.</em> | ||
</p> | </p> | ||
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<td style="background-color:#ccffcc;padding:7px;"> | <td style="background-color:#ccffcc;padding:7px;"> | ||
<p> | <p> | ||
Initialization: In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file. | <b>Initialization:</b> | ||
In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file. | |||
</p> | </p> | ||
</td> | </td> | ||
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# Vectors in the plane | # Vectors in the plane | ||
$AB = non_zero_vector3D(); | $AB = non_zero_vector3D(); | ||
$AC = non_zero_vector3D(); while (areParallel $AB $AC) {$AC = non_zero_vector3D()} | $AC = non_zero_vector3D(); | ||
while (areParallel $AB $AC) {$AC = non_zero_vector3D()} | |||
# The normal vector | # The normal vector | ||
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<td style="background-color:#ffffcc;padding:7px;"> | <td style="background-color:#ffffcc;padding:7px;"> | ||
<p> | <p> | ||
<b>Setup:</b> | |||
Create points and vectors. Make sure that the vectors are not parallel. | |||
</p> | </p> | ||
</td> | </td> | ||
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<td style="background-color:#ffcccc;padding:7px;"> | <td style="background-color:#ffcccc;padding:7px;"> | ||
<p> | <p> | ||
<b>Main Text:</b> | |||
Self-explanatory. | |||
</p> | </p> | ||
</td> | </td> | ||
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<td style="background-color:#eeccff;padding:7px;"> | <td style="background-color:#eeccff;padding:7px;"> | ||
<p> | <p> | ||
Answer Evaluation: Just specify a point $A and a normal vector $N. | <b>Answer Evaluation:</b> | ||
Just specify a point $A and a normal vector $N. | |||
</p> | </p> | ||
</td> | </td> | ||
Revision as of 21:56, 22 January 2010
Planes Defined Implicitly
This shows the PG code to evaluate answers that are planes defined implicitly by an equation.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserImplicitPlane.pl", "parserVectorUtils.pl", "PGcourse.pl", ); TEXT(beginproblem); |
Initialization:
In particular, we need to include the |
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);
|
Setup: Create points and vectors. Make sure that the vectors are not parallel. |
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(ImplicitPlane($A,$N)->cmp); $showPartialCorrectAnswers = 1; ENDDOCUMENT(); |
Answer Evaluation: Just specify a point $A and a normal vector $N. |