VectorValuedFunctions
Vector Valued Functions as Answers
This shows the PG code to check student answers that are vectors whose components are formulas.
- Example 1: Vector Parametric Lines
Example 1: Vector Parametric Lines
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserVectorUtils.pl", "parserParametricLine.pl", "answerCustom.pl", "PGcourse.pl", ); TEXT(beginproblem()); |
Initialization:
The first three macros should always be loaded for questions whose answers are vector valued functions.
For the general vector parametric line (part (a) in the question below) we need to load |
Context("Vector");
Context()->variables->are(t=>"Real");
$P = non_zero_point3D();
$disp = non_zero_vector3D();
$Q = Point($P + $disp);
$speed = random(3,9,1);
|
Setup: We randomize two points in three-dimensional space, P and Q, a displacement vector between them, and a speed to travel between them. |
Context()->texStrings;
BEGIN_TEXT
A particle starts at the point \( P = $P \)
when \( t = 0 \) and moves along a straight line
toward \( Q = $Q \) at a speed of \( $speed \)
cm/sec. Assume that x, y, and z are measured
in cm. Do not enter units with your answers.
$BR
$BR
(a) Find a vector parametric equation for the
line through points \( P \) and \( Q \).
$BR
\( L(t) = \) \{ ans_rule(40) \}
$BR
$BR
(b) Find the vector parametric equation
for the position of the object.
$BR
\( \vec{r}(t) = \) \{ans_rule(40)\}
END_TEXT
Context()->normalStrings;
|
Main Text: The problem text section of the file is as we'd expect. |
$showPartialCorrectAnswers = 1;
ANS( ParametricLine("$P + t * $disp")->cmp() );
# for checking a particular vector parametric line
sub mycheck {
my ($correct, $student, $ansHash) = @_;
if (
($correct . i == $student . i) &&
($correct . j == $student . j) &&
($correct . k == $student . k)
)
{ return 1; } else { return 0; }
}
$T = Formula("$speed * t / norm($disp)");
$r = $P + $T * $disp;
ANS( custom_cmp( $r, ~~&mycheck, showCoordinateHints=>1 ) );
ENDDOCUMENT();
|
Answer Evaluation:
The answer to part (a) can be any vector parametric line through the points P and Q, so we use
In part (b) of the question, there is only one vector parametric equation that describes the position of the object subject to the given conditions, so we want only one answer to be marked correct. We create a custom answer checker For more on custom answer evaluators, see CustomAnswerCheckers and answerCustom.pl.html |
- POD documentation: parserParametricLine.pl.html
- PG macro: parserParametricLine.pl
- POD documentation: answerCustom.pl.html
- PG macro: answerCustom.pl
