## DESCRIPTION
## Parametric equations: parametric curve in space
## ENDDESCRIPTION

## KEYWORDS('parametric', 'curve in space')

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('Fort Lewis Tutorial 2011')
## Date('01/30/2011')
## Author('Paul Pearson')
## Institution('Fort Lewis College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


#################################
#  Initialization

DOCUMENT();

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

TEXT(beginproblem());


#################################
#  Setup

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; }


}
);




#####################################
#  Main text

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;


############################
#  Answer evaluation

$showPartialCorrectAnswers = 1;

ANS( $multians->cmp() );


############################
#  Solution

Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();