VectorParametricLines1
Vector Parametric Lines
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
- PGML location in OPL: FortLewis/Authoring/Templates/Parametric/VectorParametricLines1_PGML.pg
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserVectorUtils.pl", "parserParametricLine.pl", ); TEXT(beginproblem()); |
Initialization:
We load |
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 |
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();
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Solution: |
