## DESCRIPTION
## Parametric equations: vector parametric lines
## ENDDESCRIPTION

## KEYWORDS('parametric', 'vector parametric lines')

## 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",
"parserParametricLine.pl",
);

TEXT(beginproblem());


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

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

$P = non_zero_point3D(-9,9,1);
$V = non_zero_vector3D(-9,9,1);

$Q = Point($P + $V);

$particular = Line($P,$V,'t');
$general = ParametricLine($P,$V);



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

Context()->texStrings;
BEGIN_TEXT
(a) Find a vector parametric equation for the 
line that goes through the point \( $P \) 
when \( t = 0 \) and the point \( $Q \) when
\( t = 1 \).
$BR
\( \vec{L}(t) = \)
\{ ans_rule(30) \}
$BR
$BR
(b) Find any vector parametric equation for the 
line that goes through the points \( $P \) and 
\( $Q \).
$BR
\( \vec{L}(t) = \)
\{ ans_rule(30) \}
END_TEXT
Context()->normalStrings;


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

$showPartialCorrectAnswers = 1;

ANS( $particular->cmp() );
ANS( $general->cmp() );


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

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

COMMENT('MathObject version.');

ENDDOCUMENT();