View of /trunk/NationalProblemLibrary/Rochester/setVectors2DotProduct/UR_VC_1_18.pg

    1 ## DESCRIPTION
    2 ##   Application of the Dot Product
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Dot Product', 'Projection')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('The Dot Product')
   11 ## Date('6/2/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(-3, 3);
   34 $b = random(-3, 3);
   35 $c = random(1, 2);
   36 $d = random(3, 5);
   37 $e = random(3, 5);
   38 $f = random(1, 2);
   39 
   40 $ans1 = $a + $e*($c*$e + $d*$f)/(($e)**2 + ($f)**2) ;
   41 $ans2 = $b + $f*($c*$e + $d*$f)/(($e)**2 + ($f)**2) ;
   42 
   43 BEGIN_TEXT
   44 $PAR
   45 Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates
   46 ($a, $b) and arrived in the Iron Hills at the point with coordinates (\{ $a + $c
   47 \}, \{ $b + $d \}).  If he began walking in the direction of the vector \( \bf v
   48 = $e \mathbf{i} + $f \mathbf{j} \) and changes direction only once, when he turns at a right
   49 angle, what are the coordinates of the point where he makes the turn.
   50 $PAR
   51 (\{ ans_rule(40) \}, \{ ans_rule(40) \})
   52 END_TEXT
   53 ANS(num_cmp($ans1));
   54 ANS(num_cmp($ans2));
   55 
   56 ENDDOCUMENT();