VectorParametric1

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A Vector Parametric Curve in the Plane

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This PG code shows how to ask students for a vector parametric curve through two points and allows them to specify the time interval.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"parserMultiAnswer.pl",
);

TEXT(beginproblem());

Initialization: Since it is a vector parametric curve, we will want vector utilities from parserVectorUtils.pl. Since we will need to check multiple answer blanks that depend upon each other, we use parserMultiAnswer.pl.

Context("Vector2D");
#Context("Vector"); # for 3D vectors
Context()->variables->are(t=>"Real");
Context()->variables->set(t=>{limits=>[0,5]});
Context()->flags->set( ijk=>0 );

$a = random(2,5,1);
$Q = Point($a,$a**2);


$multians = MultiAnswer(Vector("<t,t**2>"),0,$a)->with(
  singleResult => 1,

  checker => sub {

  my ($correct,$student,$self) = @_;  # get the parameters
  my ($f,$x1,$x2) = @{$student};      # extract student answers
  if ( 
       ( ($f . i)**2 == ($f . j)  )
       && ($f->eval(t=>$x1) == Vector("<0,0>")) 
       && ($f->eval(t=>$x2) == Vector("<$a,$a**2>")) 
     ) { 
       return 1; 
     } elsif (
       ( ($f . i)**2 == ($f . j)  )
       && ($f->eval(t=>$x1) == Vector("<0,0>")) 
     ) {
       $self->setMessage(3,"Your right endpoint is not correct."); 
       return 0; 
     } elsif (
       ( ($f . i)**2 == ($f . j)  )
       && ($f->eval(t=>$x2) == Vector("<$a,$a**2>")) 
     ) {
       $self->setMessage(2,"Your left endpoint is not correct."); 
       return 0; 
     } elsif (
       ( ($f . i)**2 == ($f . j)  )
     ) {
       $self->setMessage(2,"Your left endpoint is not correct."); 
       $self->setMessage(3,"Your right endpoint is not correct."); 
       return 0;
     } else { return 0; }


}
);

Setup: The student's vector-valued function is stored in $f. To get the x- and y-components of the students answer we dot it with the standard basis vectors using $f . i and $f . j. Note: If you want to differentiate the component functions in the student's answer, you'll need to use a different method as ($f . i)->D('t') will generate errors since the dot product does not get evaluated. Another problem given in this section describes how to extract formulas from the components of the student's answer, which can then be differentiated. Notice that we have given the students helpful feedback messages about which endpoints are incorrect.

Context()->texStrings;
BEGIN_TEXT
Find a vector parametric equation for the parabola
\( y = x^2 \) from the origin to the point 
\( $Q \) using \( t \) as a parameter.
$BR
$BR
\( \vec{r}(t) = \) 
\{$multians->ans_rule(20)\} 
for 
\{$multians->ans_rule(5)\} 
\( \leq t \leq \) 
\{$multians->ans_rule(5)\}
END_TEXT
Context()->normalStrings;

Main Text:

$showPartialCorrectAnswers = 1;

ANS( $multians->cmp() );

Answer Evaluation:

Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT(); 

Solution:

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