View of /trunk/NationalProblemLibrary/272/setStewart16_2/UR_VC_11_10.pg

    1 ## DESCRIPTION
    2 ##   Line Integral over Vector Field
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Vector Fields', 'Line Integral', 'Tangent', 'Normal', 'Binormal')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vector Calculus')
   10 ## DBsection('Line Integrals')
   11 ## Date('6/5/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('University of Rochester')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('16.2')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('16.2')
   24 ## Problem2('')
   25 
   26 DOCUMENT();
   27 
   28 loadMacros(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl"
   34 );
   35 
   36 TEXT(beginproblem());
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $a = random(1, 7);
   40 $b = random(1, 7);
   41 $ba = $b+ $a;
   42 
   43 BEGIN_TEXT
   44 $PAR
   45 A curve C is given by a vector function \( \mathbf{r}(t), $a \leq t \leq $ba \),
   46 with unit tangent \( \mathbf{T}(t) \), unit normal \( \mathbf{N}(t) \), and unit
   47 binormal \( \mathbf{B}(t) \).  Indicate whether the following line integrals are
   48 positive, negative, or zero by typing P, N, or Z as appropriate:
   49 $PAR
   50 A. \( \displaystyle \int_C \mathbf T \cdot \, d\mathbf r = \) \{ ans_rule(10) \}
   51 $PAR
   52 B. \( \displaystyle \int_C \mathbf N \cdot \, d\mathbf r = \) \{ ans_rule(10) \}
   53 $PAR
   54 C. \( \displaystyle \int_C \mathbf B \cdot \, d\mathbf r = \) \{ ans_rule(10) \}
   55 END_TEXT
   56 ANS(str_cmp('p'));
   57 ANS(str_cmp('z'));
   58 ANS(str_cmp('z'));
   59 
   60 ENDDOCUMENT();