View of /trunk/NationalProblemLibrary/Rochester/setVectors2DotProduct/UR_VC_1_13.pg

    1 ## DESCRIPTION
    2 ##   Angle between Vectors
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Dot Product', 'Angle')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('The Dot Product')
   11 ## Date('5/31/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('12.3')
   23 ## Problem2('28')
   24 
   25 DOCUMENT();
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 1;
   37 
   38 $a = non_zero_random(-10, 10);
   39 $b = random(-10, 10);
   40 $c = random(-10, 10);
   41 $d = non_zero_random(-10, 10);
   42 $e = random(-10, 10);
   43 $f = random(-10, 10);
   44 
   45 $adbecf = $a*$d + $b*$e + $c*$f;
   46 
   47 $dist1 = sqrt(($a)**2 + ($b)**2 + ($c)**2);
   48 $dist2 = sqrt(($d)**2 + ($e)**2 + ($f)**2);
   49 
   50 $ans = arccos($adbecf/($dist1*$dist2));
   51 
   52 BEGIN_TEXT
   53 $PAR
   54 What is the angle in radians between the vectors
   55 $BR \( {\mathbf a} \) = ($a, $b, $c)
   56 and $BR \( {\mathbf b} \) = ($d, $e, $f)?
   57 
   58 $PAR Angle: \{ ans_rule(60) \} (radians)
   59 END_TEXT
   60 ANS(num_cmp($ans));
   61 
   62 ENDDOCUMENT();