ImplicitPlane

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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