Difference between revisions of "VectorValuedFunctions"

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<b>Answer Evaluation:</b>
  
<b>Answer Evaluation:</b>
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The answer to part (a) can be any vector parametric line through the points P and Q, so we use <code>ParametricLine("$P + t * $disp")</code> provided by <code>parserParametricLine.pl</code> to allow student answers that use a different parametrization, such as <code>$P + 2t * $disp</code> to be marked correct.
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The answer to part (a) can be any vector parametric line through the points P and Q, so we use <code>ParametricLine("$P + t * $disp")</code> provided by <code>parserParametricLine.pl</code> to allow student answers that use a different parametrization, such as <code>$P + 2t * $disp</code>, to be marked correct.
 
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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 <code>mycheck</code> which is a subroutine that verifies that the student's answer agrees with the correct answer in each component by taking the dot product with the each of the vectors i, j, and k separately. We use <code>custom_cmp()</code> provided by the macro <code>answerCustom.pl</code> so that we can use it to enable the <code>showCoordinateHints=>1</code> feature.
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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 <code>mycheck</code> which is a subroutine that verifies that the student's answer agrees with the correct answer in each component by taking the dot product with the each of the vectors i, j, and k separately. We use <code>custom_cmp()</code> provided by the macro <code>answerCustom.pl</code> so that we can enable the <code>showCoordinateHints=>1</code> feature.
 
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Revision as of 18:42, 4 March 2010

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

Problem Techniques Index

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 parserParametricLine.pl, and for the specific vector parametric line (part (b) in the question below) we need to load answerCustom.pl since we will use a custom answer checker and want to have features like showCoordinateHints enabled. 

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 ParametricLine("$P + t * $disp") provided by parserParametricLine.pl to allow student answers that use a different parametrization, such as $P + 2t * $disp, to be marked correct.

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 mycheck which is a subroutine that verifies that the student's answer agrees with the correct answer in each component by taking the dot product with the each of the vectors i, j, and k separately. We use custom_cmp() provided by the macro answerCustom.pl so that we can enable the showCoordinateHints=>1 feature.

For more on custom answer evaluators, see CustomAnswerCheckers and answerCustom.pl.html

Problem Techniques Index



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