# VectorParametricLines1

## Vector Parametric Lines

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This PG code shows how to require students to enter a parametrized line that must go through certain points when t=0 and t=1, or allow them to enter an equation for any parametric line through two points.

PG problem file Explanation

Problem tagging:

DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"parserParametricLine.pl",
);

TEXT(beginproblem());

Initialization: We load parserVectorUtils.pl which provides the Line() subroutine for a particular parametrization of a line, as well as parserParametricLine.pl which provides a subroutine ParametricLine() that allows students to enter any parametrization.

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); Setup: For the answer which is a particular parametrization through two points at times t=0 and t=1, we use Line(). To allow students to enter any equation for a parametric line through two points, we use ParametricLine() The syntax is fairly self-explanatory. 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; Main Text:$showPartialCorrectAnswers = 1;

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

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

COMMENT('MathObject version.');

ENDDOCUMENT();

Solution: