Difference between revisions of "ImplicitPlane"
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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;"> |
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| − | <em>This |
+ | <em>This shows the PG code to evaluate answers that are planes defined implicitly by an equation.</em> |
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<p> |
<p> |
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| − | Initialization: In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file. |
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| + | <b>Initialization:</b> |
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| + | In particular, we need to include the <code>parserImplicitPlane.pl</code> macro file. |
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# Vectors in the plane |
# Vectors in the plane |
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$AB = non_zero_vector3D(); |
$AB = non_zero_vector3D(); |
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| − | $AC = non_zero_vector3D(); |
+ | $AC = non_zero_vector3D(); |
| + | while (areParallel $AB $AC) {$AC = non_zero_vector3D()} |
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# The normal vector |
# The normal vector |
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| − | Set-up: Create points and vectors. Make sure that the vectors are not parallel. |
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| + | <b>Setup:</b> |
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| + | Create points and vectors. Make sure that the vectors are not parallel. |
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| − | Question: self-explanatory. |
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| + | <b>Main Text:</b> |
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| + | Self-explanatory. |
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| − | Answer Evaluation: |
+ | <b>Answer Evaluation:</b> |
| + | Just specify a point $A and a normal vector $N. |
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Revision as of 17:56, 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. |
