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# View of /branches/UGA/1.5.2.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1847 byte(s)
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    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
23            "PGbasicmacros.pl",
24            "PGchoicemacros.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.