View of /branches/UGA/1.5.2.pg

    1 ## DESCRIPTION
    2 ##   Use Cross Products to Find Equation of a Plane through Three Points
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Cross Product', 'Equation of Plane')
    6 ##
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('The Cross Product')
   11 ## Date('8/22/2009')
   12 ## Author('Ted Shifrin')
   13 ## Institution('UGA')
   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("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl",
   27            "PGmatrixmacros.pl"
   28           );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(-5, 5, 1);
   34 $b = random(-5, 5, 1);
   35 $c = random(-5, 5, 1);
   36 $d = random(-2, 2, 1);
   37 $e = random(-3, 3, 1);
   38 $f = random(-3,3,1);
   39 $g = $a+$d;
   40 $h = $b+$e;
   41 $i = $c+1;
   42 $j = $g+$f;
   43 $k = $h+$e*$f-1;
   44 $l = $i+$f;
   45 
   46 $ans1 = (1-$d)*$f;
   47 $ans2 = ($d-1)*($e*$f-1)-1;
   48 $ans3 = $a+$ans1*$b+$ans2*$c;
   49 
   50 
   51 BEGIN_TEXT
   52 Find a vector with first coordinate equal to \( 1\) that is orthogonal to
   53 the plane through the points
   54 \{ mbox( display_matrix([[$a],[$b],[$c]]),",", display_matrix([[$g],[$h],[$i]]) ,  ",", "\(\quad\) and", display_matrix([[$j],[$k],[$l]]), ".") \}
   55 $BR
   56 \{ mbox( answer_matrix(3,1,6) ) \}
   57 $BR
   58 
   59 
   60 Give an equation of the plane passing through the same three points:
   61 $BR
   62 \( x \)+ \{ans_rule(6)\}\( y + \) \{ans_rule(6)\}\( z= \) \{ans_rule(6)\}. $BR
   63 (Make sure to fill in each box, even if a coefficient might happen to be \(0\).) $BR
   64 END_TEXT
   65 
   66 ANS(num_cmp(1));
   67 ANS(num_cmp($ans1));
   68 ANS(num_cmp($ans2));
   69 
   70 ANS(num_cmp($ans1));
   71 ANS(num_cmp($ans2));
   72 ANS(num_cmp($ans3));
   73 
   74 ENDDOCUMENT();  # This should be the last executable line in the problem.