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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 ## Tagged by nhamblet 6 : jj 140 7 : jjholt 205 ## DBsubject('Calculus') 8 : ## DBchapter('Vectors and the Geometry of Space') 9 : ## DBsection('The Dot Product') 10 : jj 3115 ## Date('6/3/2002') 11 : ## TitleText1('Calculus: Early Transcendentals') 12 : ## AuthorText1('Rogawski') 13 : ## EditionText1('1') 14 : ## Section1('12.3') 15 : ## Problem1('28') 16 : sh002i 556 ## TitleText2('Calculus: Early Transcendentals') 17 : jj 3115 ## AuthorText2('Stewart') 18 : ## EditionText2('6') 19 : sh002i 556 ## Section2('12.3') 20 : ## Problem2('28') 21 : jj 3115 ## KEYWORDS('Dot Product', 'Angle',"vector') 22 : jjholt 205 23 : jj 140 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 : $PAR 52 : What is the angle in radians between the vectors 53 : jjholt 482$BR $${\mathbf a}$$ = ($a,$b, $c) 54 : and$BR $${\mathbf b}$$ = ($d,$e, $f)? 55 : jj 140 56 :$PAR Angle: \{ ans_rule(60) \} (radians) 57 : END_TEXT 58 : ANS(num_cmp(\$ans)); 59 : 60 : ENDDOCUMENT();