VectorParametricLines1

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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.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();

loadMacros(
"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() );

Answer Evaluation:

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

COMMENT('MathObject version.');

ENDDOCUMENT();

Solution:

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