View of /branches/UGA/1.2.4.pg

    1 ## DESCRIPTION
    2 ##   Dot Product
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Dot Product', 'Angle')
    6 
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('Dot Product')
   11 ## Date('5/27/10')
   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 $a = random(1,4);
   40 do{$b = random(1,4)} until ($b != $a);
   41 
   42 do{$c = non_zero_random(-3,3)} until ($c**2!=1);
   43 do{$d = non_zero_random(-3,3)} until ($d!=$c && $d!=-$c && $d**2!=1);
   44 
   45 $m = $a*$b*($c+$d);
   46 
   47 $ans1 = Real("sqrt(($a)^2+($c*$b)^2+ 2*$c/($c+$d))");
   48 $ans2 = Real("sqrt(($a)^2+($b*$d)^2+ 2*$d/($c+$d))");
   49 $ans3 = Real("arccos((($a)^2+$c*$d*($b)^2 + 1)/($ans1*$ans2))");
   50 
   51 Context()->texStrings;
   52 BEGIN_TEXT
   53 
   54 If \(\|\mathbf x\| = $a\), \(\|\mathbf y\| = $b\), and the angle between \(\mathbf x\) and \(\mathbf y\) is \(\theta = \arccos(1/$m)\), then
   55 $PAR
   56 (a) \(\|\mathbf x + $c\mathbf y\| = \) \{ans_rule(15)\}
   57 $PAR
   58 (b) \(\|\mathbf x + $d\mathbf y\| = \) \{ans_rule(15)\}
   59 $PAR
   60 (c) and the angle
   61 between the vectors \(\mathbf x + $c\mathbf y\) and \(\mathbf x + $d\mathbf y\) is (in radians) \{ans_rule(20)\}
   62 
   63 
   64 END_TEXT
   65 
   66 ANS($ans1->cmp,$ans2->cmp,$ans3->cmp);
   67 
   68 ENDDOCUMENT();