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# Annotation of /trunk/NationalProblemLibrary/Rochester/setVectors2DotProduct/UR_VC_1_13.pg

 1 : jjholt 205 ## DESCRIPTION 2 : ## Angle between Vectors 3 : ## ENDDESCRIPTION 4 : jj 140 5 : jjholt 205 ## KEYWORDS('Dot Product', 'Angle') 6 : ## Tagged by nhamblet 7 : jj 140 8 : jjholt 205 ## 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 : jj 140 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();