ImplicitPlane
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Planes Defined Implicitly: PG Code Snippet
This code snippet shows the PG code to evaluate answers that are planes defined implicitly by an equation.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "PGunion.pl", "MathObjects.pl", "parserImplicitPlane.pl", "parserVectorUtils.pl", "PGcourse.pl", ); TEXT(beginproblem); |
Initialization: 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;
# The points A, B and C
$A = non_zero_point3D();
$B = Point($A + $AB);
$C = Point($A + $AC);
|
Set-up: 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;
|
Question: self-explanatory. |
ANS(ImplicitPlane($A,$N)->cmp); $showPartialCorrectAnswers = 1; ENDDOCUMENT(); |
Answer Evaluation: Just specify a point $A and a normal vector $N. |
