ImplicitPlane1

Answer is an Equation for a Line or Plane

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This PG code shows how to define an answer that is a line or plane.

• File location in OPL: FortLewis/Authoring/Templates/DiffCalcMV/ImplicitPlane1.pg
• PGML location in OPL: FortLewis/Authoring/Templates/DiffCalcMV/ImplicitPlane1_PGML.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( 'PGstandard.pl', 'MathObjects.pl', 'parserImplicitPlane.pl', 'parserVectorUtils.pl', 'PGML.pl', 'PGcourse.pl' ); TEXT(beginproblem());	Initialization: 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(-5,5,1); $N = non_zero_vector3D(-5,5,1); $answer1 = ImplicitPlane($A,$N); $answer2 = ImplicitPlane('4x+3y=12'); $answer3 = ImplicitPlane('x=3');	Setup: The first answer is a standard mulitivariable calculus question. There are several different ways to specify the input to ImplicitPlane, which are detailed in the POD documentation. It is also possible to do some more complicated manipulations with the vectors and points, which is detailed in the problem techniques section. When the ImplicitPlane context has only two variables, it rephrases error messages in terms of lines. If you want students to be able to enter an equation for a line in the most general form, or if you have a vertical line to check (or just a constant equation such as x=3), you can use the ImplicitPlane context to reliably check these answers.
BEGIN_PGML a. Enter an equation for the plane through the point [` [$A] `] and perpendicular to [` [$N] `]. + [______________]{$answer1} b. Enter an equation for the line in the [` xy `]-plane with [` x `]-intercept [` 3 `] and [` y `]-intercept [` 4 `]. + [______________]{$answer2} c. Enter an equation for the vertical line in the [` xy `]-plane through the point [` (3,1) `]. + [______________]{$answer3} [@ helpLink('equation') @]* END_PGML	Main Text:
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION	Solution:

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