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# View of /branches/UGA/1.2.4.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1611 byte(s)
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    1 ## DESCRIPTION
2 ##   Dot Product
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Dot Product', 'Angle')
6
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vectors and the Geometry of Space')
10 ## DBsection('Dot Product')
11 ## Date('5/27/10')
12 ## Author('Ted Shifrin'
13 ## Institution('UGA')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();
21
23            "PGbasicmacros.pl",
24            "PGchoicemacros.pl",
26            "PGauxiliaryFunctions.pl",
27            "PGmatrixmacros.pl",
28            "PGmorematrixmacros.pl",
29            "Parser.pl",
30            "MathObjects.pl",
31            );
32
33 TEXT(beginproblem());
34 $showPartialCorrectAnswers = 1; 35 36 Context("Vector"); 37 38 39$a = random(1,4);
40 do{$b = random(1,4)} until ($b != $a); 41 42 do{$c = non_zero_random(-3,3)} until ($c**2!=1); 43 do{$d = non_zero_random(-3,3)} until ($d!=$c && $d!=-$c && $d**2!=1); 44 45$m = $a*$b*($c+$d);
46
47 $ans1 = Real("sqrt(($a)^2+($c*$b)^2+ 2*$c/($c+$d))"); 48$ans2 = Real("sqrt(($a)^2+($b*$d)^2+ 2*$d/($c+$d))");
49 $ans3 = Real("arccos((($a)^2+$c*$d*($b)^2 + 1)/($ans1*$ans2))"); 50 51 Context()->texStrings; 52 BEGIN_TEXT 53 54 If $$\|\mathbf x\| = a$$, $$\|\mathbf y\| = b$$, and the angle between $$\mathbf x$$ and $$\mathbf y$$ is $$\theta = \arccos(1/m)$$, then 55$PAR
56 (a) $$\|\mathbf x + c\mathbf y\| =$$ \{ans_rule(15)\}
57 $PAR 58 (b) $$\|\mathbf x + d\mathbf y\| =$$ \{ans_rule(15)\} 59$PAR
60 (c) and the angle
61 between the vectors $$\mathbf x + c\mathbf y$$ and $$\mathbf x + d\mathbf y$$ is (in radians) \{ans_rule(20)\}
62
63
64 END_TEXT
65
66 ANS($ans1->cmp,$ans2->cmp,\$ans3->cmp);
67
68 ENDDOCUMENT();