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| 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(); |
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