## DESCRIPTION ## Vector Addition and Parallelograms ## ENDDESCRIPTION ## KEYWORDS('Vector Addition', 'Parallelogram') ## DBsubject('Calculus') ## DBchapter('Vectors and the Geometry of Space') ## DBsection('Vector Algebra') ## Date('5/12/10') ## Author('Ted Shifrin' ## Institution('UGA') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); loadMacros("PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGmatrixmacros.pl", "PGmorematrixmacros.pl", "Parser.pl", "MathObjects.pl", ); TEXT(beginproblem()); \$showPartialCorrectAnswers = 1; Context("Vector"); \$a = random(-3,3); \$b = random(-3,3); \$c = random(-3,3); \$d = non_zero_random(-3,3); \$e = non_zero_random(-3,3); \$f = non_zero_random(-3,3); \$a2 = \$a+\$d; \$b2 = \$b+\$e; \$c2 = \$c+\$f; do{\$g = non_zero_random(-3,3)} until (\$g!=\$d); do{\$h = non_zero_random(-3,3)} until (\$h!=\$e); do{\$i = non_zero_random(-3,3)} until (\$i!=\$f); \$a3 = \$a+\$g; \$b3 = \$b+\$h; \$c3 = \$c+\$i; \$P = ColumnVector("<\$a,\$b,\$c>"); \$Q = ColumnVector("<\$a2,\$b2,\$c2>"); \$R = ColumnVector("<\$a3,\$b3,\$c3>"); \$A1 = \$a2+\$g; \$A2 = \$b2+\$h; \$A3 = \$c2+\$i; \$B1 = \$a2-\$g; \$B2 = \$b2-\$h; \$B3 = \$c2-\$i; \$C1 = \$a3-\$d; \$C2 = \$b3-\$e; \$C3 = \$c3-\$f; \$A = Vector("<\$A1,\$A2,\$A3>"); \$B = Vector("<\$B1,\$B2,\$B3>"); \$C = Vector("<\$C1,\$C2,\$C3>"); \$ans = List(Compute("\$A"),Compute("\$B"),Compute("\$C")); Context()->texStrings; BEGIN_TEXT Three vertices of a parallelogram are at \$PAR \(\$P\), \(\$Q\), and \(\$R\). \$BR \$PAR What are the \$BBOLD three \$EBOLD possible locations of the fourth vertex? \$PAR 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. \$BR \{ans_rule(50)\} END_TEXT ANS(\$ans->cmp); ENDDOCUMENT();