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

 1 : jj 140 ##DESCRIPTION 2 : # First Created: 5/31/00 3 : # Last Modified: 6/1/00 4 : # Author: Joseph Neisendorfer 5 : # WebworK Entry: Robert Van Dam 6 : # Location: University of Rochester 7 : # 8 : # Math 164 Problems - Assignment 1 - Problem 13 9 : ##ENDDESCRIPTION 10 : 11 : ##KEYWORDS("vector') 12 : 13 : DOCUMENT(); 14 : 15 : loadMacros( 16 : "PG.pl", 17 : "PGbasicmacros.pl", 18 : "PGchoicemacros.pl", 19 : "PGanswermacros.pl", 20 : "PGauxiliaryFunctions.pl" 21 : ); 22 : 23 : TEXT(beginproblem()); 24 : $showPartialCorrectAnswers = 1; 25 : 26 :$a = non_zero_random(-10, 10); 27 : $b = random(-10, 10); 28 :$c = random(-10, 10); 29 : $d = non_zero_random(-10, 10); 30 :$e = random(-10, 10); 31 : $f = random(-10, 10); 32 : 33 :$adbecf = $a*$d + $b*$e + $c*$f; 34 : 35 : $dist1 = sqrt(($a)**2 + ($b)**2 + ($c)**2); 36 : $dist2 = sqrt(($d)**2 + ($e)**2 + ($f)**2); 37 : 38 : $ans = arccos($adbecf/($dist1*$dist2)); 39 : 40 : BEGIN_TEXT 41 : $PAR 42 : What is the angle in radians between the vectors 43 :$BR $${\bf a}$$ = ($a,$b, $c) 44 : and$BR $${\bf b}$$ = ($d,$e, $f)? 45 : 46 :$PAR Angle: \{ ans_rule(60) \} (radians) 47 : END_TEXT 48 : ANS(num_cmp(\$ans)); 49 : 50 : ENDDOCUMENT();