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| 1 : | ted shifri | 1457 | ## DESCRIPTION |
| 2 : | ## Vector Addition and Parallelograms | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('Vector Addition', 'Parallelogram') | ||
| 6 : | |||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Vectors and the Geometry of Space') | ||
| 10 : | ## DBsection('Vector Algebra') | ||
| 11 : | ## Date('5/12/10') | ||
| 12 : | ## Author('Ted Shifrin' | ||
| 13 : | ## Institution('UGA') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | DOCUMENT(); | ||
| 21 : | |||
| 22 : | loadMacros("PG.pl", | ||
| 23 : | "PGbasicmacros.pl", | ||
| 24 : | "PGchoicemacros.pl", | ||
| 25 : | "PGanswermacros.pl", | ||
| 26 : | "PGauxiliaryFunctions.pl", | ||
| 27 : | "PGmatrixmacros.pl", | ||
| 28 : | "PGmorematrixmacros.pl", | ||
| 29 : | "Parser.pl", | ||
| 30 : | "MathObjects.pl", | ||
| 31 : | ); | ||
| 32 : | |||
| 33 : | TEXT(beginproblem()); | ||
| 34 : | $showPartialCorrectAnswers = 1; | ||
| 35 : | |||
| 36 : | Context("Vector"); | ||
| 37 : | |||
| 38 : | |||
| 39 : | $a = random(-3,3); | ||
| 40 : | $b = random(-3,3); | ||
| 41 : | $c = random(-3,3); | ||
| 42 : | $d = non_zero_random(-3,3); | ||
| 43 : | $e = non_zero_random(-3,3); | ||
| 44 : | $f = non_zero_random(-3,3); | ||
| 45 : | $a2 = $a+$d; | ||
| 46 : | $b2 = $b+$e; | ||
| 47 : | $c2 = $c+$f; | ||
| 48 : | do{$g = non_zero_random(-3,3)} until ($g!=$d); | ||
| 49 : | do{$h = non_zero_random(-3,3)} until ($h!=$e); | ||
| 50 : | do{$i = non_zero_random(-3,3)} until ($i!=$f); | ||
| 51 : | $a3 = $a+$g; | ||
| 52 : | $b3 = $b+$h; | ||
| 53 : | $c3 = $c+$i; | ||
| 54 : | |||
| 55 : | $P = ColumnVector("<$a,$b,$c>"); | ||
| 56 : | $Q = ColumnVector("<$a2,$b2,$c2>"); | ||
| 57 : | $R = ColumnVector("<$a3,$b3,$c3>"); | ||
| 58 : | |||
| 59 : | $A1 = $a2+$g; | ||
| 60 : | $A2 = $b2+$h; | ||
| 61 : | $A3 = $c2+$i; | ||
| 62 : | $B1 = $a2-$g; | ||
| 63 : | $B2 = $b2-$h; | ||
| 64 : | $B3 = $c2-$i; | ||
| 65 : | $C1 = $a3-$d; | ||
| 66 : | $C2 = $b3-$e; | ||
| 67 : | $C3 = $c3-$f; | ||
| 68 : | |||
| 69 : | $A = Vector("<$A1,$A2,$A3>"); | ||
| 70 : | $B = Vector("<$B1,$B2,$B3>"); | ||
| 71 : | $C = Vector("<$C1,$C2,$C3>"); | ||
| 72 : | |||
| 73 : | $ans = List(Compute("$A"),Compute("$B"),Compute("$C")); | ||
| 74 : | |||
| 75 : | |||
| 76 : | Context()->texStrings; | ||
| 77 : | BEGIN_TEXT | ||
| 78 : | |||
| 79 : | Three vertices of a parallelogram are at | ||
| 80 : | $PAR | ||
| 81 : | \($P\), \($Q\), and \($R\). | ||
| 82 : | $BR | ||
| 83 : | |||
| 84 : | $PAR | ||
| 85 : | What are the $BBOLD three $EBOLD possible locations of the fourth vertex? | ||
| 86 : | $PAR | ||
| 87 : | |||
| 88 : | Enter your answer as a list, with vectors written using the notation <\(a,b,c\)> (unlike our usual column vector notation) and separated by commas. | ||
| 89 : | $BR | ||
| 90 : | \{ans_rule(50)\} | ||
| 91 : | |||
| 92 : | END_TEXT | ||
| 93 : | |||
| 94 : | ANS($ans->cmp); | ||
| 95 : | |||
| 96 : | ENDDOCUMENT(); | ||
| 97 : | |||
| 98 : |
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