ImplicitPlane

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

• POD documentation: parserImplicitPlane.pl.html
• PG macro code: parserImplicitPlane.pl

• POD documentation: parserVectorUtils.pl.html
• PG macro code: parserVectorUtils.pl