## 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();