Implicit Plane

Multivariable differential calculus: answer is an equation for a plane

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

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

Preamble

The parserVectorUtils.pl macro is used for the non_zero_point3D function below.
The parserImplicitPlane.pl macro includes the context and the ImplicitPlane function to parse and create implicit planes.

Context('ImplicitPlane');
Context()->variables->are(x => 'Real', y => 'Real', z => 'Real');

$A = non_zero_point3D(-5, 5);
$N = non_zero_vector3D(-5, 5);

$ans1 = ImplicitPlane($A, $N);
$ans2 = ImplicitPlane('4x + 3y = 12');
$ans3 = ImplicitPlane('x = 3');

Setup

The first answer is a standard mulitivariable calculus question. There are several different ways to specify the input to ImplicitPlane, which are detailed in the POD documentation. It is also possible to do some more complicated manipulations with the vectors and points, which is detailed in the problem techniques section.

When the ImplicitPlane context has only two variables, it rephrases error messages in terms of lines. If you want students to be able to enter an equation for a line in the most general form, or if you have a vertical line to check (or just a constant equation such as x = 3), you can use the ImplicitPlane context to reliably check these answers.

BEGIN_PGML
a. Enter an equation for the plane through the point [`[$A]`] and perpendicular
to [`[$N]`].

    + [_]{$ans1}{15}

b. Enter an equation for the line in the [`xy`]-plane with [`x`]-intercept [`3`]
and [`y`]-intercept [`4`].

    + [_]{$ans2}{15}

c. Enter an equation for the vertical line in the [`xy`]-plane through the
point [`(3,1)`].

    + [_]{$ans3}{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.