View of /trunk/rochester_problib/instructiveProblems/OldProblems/UR_VC_1_8.pg

    1 ##DESCRIPTION
    2 #  First Created: 5/30/00
    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 8
    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 "PGcourse.pl",
   22 # "source.pl",
   23 );
   24 
   25 TEXT(beginproblem());
   26 $showPartialCorrectAnswers = 1;
   27 
   28 ###################
   29 #
   30 #  Setup
   31 
   32 $a = random(-10, 10);
   33 $b = random(-10, 10);
   34 $c = random(-10, 10);
   35 $d = random(-10, 10);
   36 $e = random(-10, 10);
   37 $f = random(-10, 10);
   38 $g = random(-10, 10);
   39 
   40 $abs = sqrt(($a)**2 + ($b)**2 + ($c)**2);
   41 
   42 ###################
   43 #
   44 #  Text
   45 
   46 BEGIN_TEXT
   47 $PAR
   48 Let \( \bf a \) = ($a, $b, $c) and \( \bf b \) = ($d, $e, $f) be vectors.  Compute the following
   49 vectors.
   50 
   51 $PAR A. \( \bf a \) + \( \bf b \) = (\{ ans_rule(6) \}, \{ ans_rule(6) \},
   52 \{ ans_rule(6) \})
   53 
   54 $PAR
   55 B. ${g}\( \bf{a} \)= (\{ ans_rule(6) \}, \{ ans_rule(6) \}, \{
   56 ans_rule(6) \})
   57 
   58 $PAR
   59 C. \( \bf a \) - \( \bf b \)= (\{ ans_rule(6) \}, \{ ans_rule(6) \}, \{
   60 ans_rule(6) \})
   61 
   62 $PAR
   63 D. \( \left|{\bf a}\right| \) = \{ ans_rule(40) \}
   64 END_TEXT
   65 
   66 ###################
   67 #
   68 #  Answers
   69 
   70 
   71 ANS(num_cmp($a+$d));
   72 ANS(num_cmp($b+$e));
   73 ANS(num_cmp($c+$f));
   74 
   75 ANS(num_cmp($g*$a));
   76 ANS(num_cmp($g*$b));
   77 ANS(num_cmp($g*$c));
   78 
   79 ANS(num_cmp($a-$d));
   80 ANS(num_cmp($b-$e));
   81 ANS(num_cmp($c-$f));
   82 
   83 ANS(num_cmp($abs));
   84 
   85 ENDDOCUMENT();