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# Annotation of /branches/UGA/1.5.2.pg

 1 : ted shifri 1457 ## 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.