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.

• File location in OPL: FortLewis/Authoring/Templates/Parametric/VectorParametricLines1.pg

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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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