Parametric Vector Function with Derivative

Parametric equations: parametric curve in space

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Complete Code

Download file: VectorParametricDerivative.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'parserVectorUtils.pl', 'PGcourse.pl');

Preamble

Although not necessary for the code below, we load parserVectorUtils.pl because you may want to use some of its methods when you use this template file.

Context('Vector2D');
Context()->variables->are(t => 'Real');
Context()->variables->set(t => { limits => [ 0, 5 ] });
Context()->flags->set(ijk => 0, ijkAnyDimension => 1);

$ans = Vector("<2t,(2t)^2>")->cmp(
    checker => sub {
        my ($correct, $student, $ansHash) = @_;
        my $xstu = $student . Vector(1, 0);
        my $ystu = $student . Vector(0, 1);
        return (($xstu->D('t') == Formula('2'))
                && ($ystu->D('t') == Formula('8t'))) ? 1 : 0;
    }
);

Setup

We choose not to display the answer using ijk notation. Also, use ijkAnyDimension => 1 to require a dimension match between i,j,k vectors and either the student or the correct answer when doing vector operations.

The custom answer checker is used to check if the derivative matching the questioned asked. Use dot products of the student answer with the vectors Vector(1,0) and Vector(0,1) to get the components $xstu and $ystu of the student answer. Then, we can differentiate the components just like any MathObject formula.

BEGIN_PGML
Find a vector parametric function [`\vec{r}(t)`]
for a bug that moves along the parabola [`y = x^2`]
with velocity [`\vec{v}(t) = \langle 2, 8t \rangle`]
for all [`t`].

[`\vec{r}(t) =`] [_]{$ans}{15}
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.