Difference between revisions of "ImplicitPlane"

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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.</em>
 
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Revision as of 20:30, 6 February 2010

Planes 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);

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.

Problem Techniques Index