View of /trunk/NationalProblemLibrary/TCNJ/TCNJ_LengthOrthogonality/problem6.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('inner product' 'orthogonal' 'angle')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Vector Spaces')
   10 ## DBsection('Inner Product')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('TCNJ')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGanswermacros.pl",
   26 "PGauxiliaryFunctions.pl",
   27 "PGmatrixmacros.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $prod = 0;
   34 $norm_x = 0;
   35 $norm_y = 0;
   36 
   37 foreach $i (0..1) {
   38   $x[$i] = non_zero_random(-5,5,1);
   39   $y[$i] = non_zero_random(-5,5,1);
   40   if ($y[$i] == $x[$i]) {
   41     $y[$i] = 6;
   42   }
   43   $prod += $x[$i] * $y[$i];
   44     $norm_x += $x[$i] * $x[$i];
   45     $norm_y += $y[$i] * $y[$i];
   46 }
   47 
   48 $norm_x = sqrt($norm_x);
   49 $norm_y = sqrt($norm_y);
   50 
   51 $angle = arccos( $prod / $norm_x / $norm_y);
   52 
   53 BEGIN_TEXT
   54 
   55 Find the angle \( \alpha \) between the vectors
   56 \{ mbox( display_matrix([[$x[0]], [$x[1]]]), ' and ', display_matrix([[$y[0]], [$y[1]]]), '.' ) \}
   57 $BR
   58 \( \alpha = \) \{ans_rule(20)\}.
   59 
   60 END_TEXT
   61 
   62 ANS(num_cmp($angle));
   63 
   64 
   65 ENDDOCUMENT();       # This should be the last executable line in the problem.
   66