Difference between revisions of "VectorValuedFunctions"

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Line 95: Line 95:
 
(a) Find any vector parametric equation for the
 
(a) Find any vector parametric equation for the
 
line through points \( P \) and \( Q \).
  
line through points \( P \) and \( Q \).
  +
$BR
 
\( L(t) = \) \{ ans_rule(40) \}
  
\( L(t) = \) \{ ans_rule(40) \}
 
$BR
  
$BR

Revision as of 18:09, 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: To do ..(what you are doing)........., we don't have to change the tagging and documentation section of the problem file. In the initialization section, we need to include the macros file -------.pl. 

Context("Vector");
Context()->variables->are(t=>"Real");

$P = non_zero_point3D();
$V = non_zero_vector3D();
$Q = Point($P + $V);
$speed = random(3,9,1);

Setup: We specify that the Context should be ......, and define the answer to be a formula.

Notes: on using this and related Contexts. 

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.
$BR
$BR
(a) Find any vector parametric equation for the 
line through points \( P \) and \( Q \).
$BR
\( L(t) = \) \{ ans_rule(40) \}
$BR
$BR
(b) Find a 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;

$T = Formula("$speed * t / norm($V)");
$L = $P + $T * $V;

ANS( ParametricLine("$L")->cmp() );


sub mycheck {
  my ($correct, $student, $ansHash) = @_;

  if ( 
       ($correct . i == $student . i) && 
       ($correct . j == $student . j) && 
       ($correct . k == $student . k) 
     ) 
  { return 1; } else { return 0; }

}

ANS( custom_cmp( $L, ~~&mycheck, showCoordinateHints=>1 ) );

ENDDOCUMENT();

Answer Evaluation:

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

Problem Techniques Index



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