ImplicitPlane
Planes or Lines Defined Implicitly
This shows the PG code to evaluate answers that are planes or lines defined implicitly by an equation.
You may also be interested in EquationsDefiningFunctions
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.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);
$answer = ImplicitPlane($A,$N);
|
Setup: Create points and vectors. Make sure that the vectors are not parallel. There are several other ways to define planes implicitly, which are explained at parserImplicitPlane.pl If the correct answer is a line in 2D space instead of a plane in 3D space, the only modification needed is to reduce the number of variables to two, which will modify error messages accordingly. Context("ImplicitPlane");
Context()->variables->are(x=>"Real",y=>"Real");
$answer = ImplicitPlane("y=4x+3");
|
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( $answer->cmp ); $showPartialCorrectAnswers = 1; ENDDOCUMENT(); |
Answer Evaluation: Just specify a point $A and a normal vector $N. |
- POD documentation: parserImplicitPlane.pl
- PG macro code: parserImplicitPlane.pl
- POD documentation: parserVectorUtils.pl
- PG macro code: parserVectorUtils.pl
