View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/12_Vector_Geometry/12.2_Vectors_in_Three_Dimensions/12.2.1.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Introduction to Differential Equations')
    3 ## DBsection('Vectors in Three Dimensions')
    4 ## KEYWORDS('calculus', 'parametric', 'vector', '3D', 'three dimensions')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('12.2')
    9 ## Problem1('1')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("PGchoicemacros.pl");
   16 loadMacros("Parser.pl");
   17 loadMacros("freemanMacros.pl");
   18 $context = Context("Vector");
   19 
   20 $a = Real(random(1,10,1));
   21 $b = Real(random(1,10,1));
   22 $c = Real(random(1,10,1));
   23 
   24 $vec = Vector($a, $b, $c);
   25 
   26 $sq = $a**2 + $b**2 + $c**2;
   27 $ans = sqrt($sq);
   28 
   29 
   30 Context()->texStrings;
   31 BEGIN_TEXT
   32 \{ beginproblem() \}
   33 \{ textbook_ref_exact("Rogawski ET 2e", "12.2","1") \}
   34 $PAR
   35 Find the length of the vector \( \mathbf{v} = $vec \).
   36 $PAR
   37 \( \| \mathbf{v} \| \)  = \{ans_rule()\}
   38 END_TEXT
   39 Context()->normalStrings;
   40 
   41 ANS($ans->cmp);
   42 
   43 Context()->texStrings;
   44 SOLUTION(EV3(<<'END_SOLUTION'));
   45 $PAR
   46 $SOL
   47 \( \| \mathbf{v} \| = \sqrt{\mathbf{v} \cdot \mathbf{v}}
   48 = \sqrt{$a \cdot $a + $b \cdot $b + $c \cdot $c}=\sqrt{$sq} \).
   49 END_SOLUTION
   50 
   51 ENDDOCUMENT();
   52 
   53