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| 1 : | pearson | 1606 | ## DESCRIPTION |
| 2 : | ## Parametric equations: vector parametric lines | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('parametric', 'vector parametric lines') | ||
| 6 : | |||
| 7 : | ## DBsubject('WeBWorK') | ||
| 8 : | ## DBchapter('WeBWorK Tutorial') | ||
| 9 : | ## DBsection('Fort Lewis Tutorial 2011') | ||
| 10 : | ## Date('01/30/2011') | ||
| 11 : | ## Author('Paul Pearson') | ||
| 12 : | ## Institution('Fort Lewis College') | ||
| 13 : | ## TitleText1('') | ||
| 14 : | ## EditionText1('') | ||
| 15 : | ## AuthorText1('') | ||
| 16 : | ## Section1('') | ||
| 17 : | ## Problem1('') | ||
| 18 : | |||
| 19 : | |||
| 20 : | ################################# | ||
| 21 : | # Initialization | ||
| 22 : | |||
| 23 : | DOCUMENT(); | ||
| 24 : | |||
| 25 : | loadMacros( | ||
| 26 : | "PGstandard.pl", | ||
| 27 : | "MathObjects.pl", | ||
| 28 : | "parserVectorUtils.pl", | ||
| 29 : | "parserParametricLine.pl", | ||
| 30 : | ); | ||
| 31 : | |||
| 32 : | TEXT(beginproblem()); | ||
| 33 : | |||
| 34 : | |||
| 35 : | ################################# | ||
| 36 : | # Setup | ||
| 37 : | |||
| 38 : | Context("Vector")->variables->are(t=>"Real"); | ||
| 39 : | |||
| 40 : | $P = non_zero_point3D(-9,9,1); | ||
| 41 : | $V = non_zero_vector3D(-9,9,1); | ||
| 42 : | |||
| 43 : | $Q = Point($P + $V); | ||
| 44 : | |||
| 45 : | $particular = Line($P,$V,'t'); | ||
| 46 : | $general = ParametricLine($P,$V); | ||
| 47 : | |||
| 48 : | |||
| 49 : | |||
| 50 : | ##################################### | ||
| 51 : | # Main text | ||
| 52 : | |||
| 53 : | Context()->texStrings; | ||
| 54 : | BEGIN_TEXT | ||
| 55 : | (a) Find a vector parametric equation for the | ||
| 56 : | line that goes through the point \( $P \) | ||
| 57 : | when \( t = 0 \) and the point \( $Q \) when | ||
| 58 : | \( t = 1 \). | ||
| 59 : | $BR | ||
| 60 : | \( \vec{L}(t) = \) | ||
| 61 : | \{ ans_rule(30) \} | ||
| 62 : | $BR | ||
| 63 : | $BR | ||
| 64 : | (b) Find any vector parametric equation for the | ||
| 65 : | line that goes through the points \( $P \) and | ||
| 66 : | \( $Q \). | ||
| 67 : | $BR | ||
| 68 : | \( \vec{L}(t) = \) | ||
| 69 : | \{ ans_rule(30) \} | ||
| 70 : | END_TEXT | ||
| 71 : | Context()->normalStrings; | ||
| 72 : | |||
| 73 : | |||
| 74 : | ############################ | ||
| 75 : | # Answer evaluation | ||
| 76 : | |||
| 77 : | $showPartialCorrectAnswers = 1; | ||
| 78 : | |||
| 79 : | ANS( $particular->cmp() ); | ||
| 80 : | ANS( $general->cmp() ); | ||
| 81 : | |||
| 82 : | |||
| 83 : | ############################ | ||
| 84 : | # Solution | ||
| 85 : | |||
| 86 : | Context()->texStrings; | ||
| 87 : | BEGIN_SOLUTION | ||
| 88 : | ${PAR}SOLUTION:${PAR} | ||
| 89 : | Solution explanation goes here. | ||
| 90 : | END_SOLUTION | ||
| 91 : | Context()->normalStrings; | ||
| 92 : | |||
| 93 : | COMMENT('MathObject version.'); | ||
| 94 : | |||
| 95 : | ENDDOCUMENT(); |
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