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 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = non_zero_random(-10, 10);
   34 $b = random(-10, 10);
   35 $c = random(-10, 10);
   36 $d = non_zero_random(-10, 10);
   37 $e = random(-10, 10);
   38 $f = random(-10, 10);
   39 
   40 $adbecf = $a*$d + $b*$e + $c*$f;
   41 
   42 $dist1 = sqrt(($a)**2 + ($b)**2 + ($c)**2);
   43 $dist2 = sqrt(($d)**2 + ($e)**2 + ($f)**2);
   44 
   45 $ans = arccos($adbecf/($dist1*$dist2));
   46 
   47 BEGIN_TEXT
   48 $PAR
   49 What is the angle in radians between the vectors
   50 $BR \( {\bf a} \) = ($a, $b, $c)
   51 and $BR \( {\bf b} \) = ($d, $e, $f)?
   52 
   53 $PAR Angle: \{ ans_rule(60) \} (radians)
   54 END_TEXT
   55 ANS(num_cmp($ans));
   56 
   57 ENDDOCUMENT();