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

    1 ## DESCRIPTION
    2 ##   Angle between Vectors
    3 ## ENDDESCRIPTION
    4 
    5 ## Tagged by nhamblet
    6 
    7 ## DBsubject('Calculus')
    8 ## DBchapter('Vectors and the Geometry of Space')
    9 ## DBsection('The Dot Product')
   10 ## Date('6/3/2002')
   11 ## TitleText1('Calculus: Early Transcendentals')
   12 ## AuthorText1('Rogawski')
   13 ## EditionText1('1')
   14 ## Section1('12.3')
   15 ## Problem1('28')
   16 ## TitleText2('Calculus: Early Transcendentals')
   17 ## AuthorText2('Stewart')
   18 ## EditionText2('6')
   19 ## Section2('12.3')
   20 ## Problem2('28')
   21 ## KEYWORDS('Dot Product', 'Angle',"vector')
   22 
   23 DOCUMENT();
   24 
   25 loadMacros(
   26 "PG.pl",
   27 "PGbasicmacros.pl",
   28 "PGchoicemacros.pl",
   29 "PGanswermacros.pl",
   30 "PGauxiliaryFunctions.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $a = non_zero_random(-10, 10);
   37 $b = random(-10, 10);
   38 $c = random(-10, 10);
   39 $d = non_zero_random(-10, 10);
   40 $e = random(-10, 10);
   41 $f = random(-10, 10);
   42 
   43 $adbecf = $a*$d + $b*$e + $c*$f;
   44 
   45 $dist1 = sqrt(($a)**2 + ($b)**2 + ($c)**2);
   46 $dist2 = sqrt(($d)**2 + ($e)**2 + ($f)**2);
   47 
   48 $ans = arccos($adbecf/($dist1*$dist2));
   49 
   50 BEGIN_TEXT
   51 $PAR
   52 What is the angle in radians between the vectors
   53 $BR \( {\mathbf a} \) = ($a, $b, $c)
   54 and $BR \( {\mathbf b} \) = ($d, $e, $f)?
   55 
   56 $PAR Angle: \{ ans_rule(60) \} (radians)
   57 END_TEXT
   58 ANS(num_cmp($ans));
   59 
   60 ENDDOCUMENT();