## DESCRIPTION
##   Angle between Vectors
## ENDDESCRIPTION

## KEYWORDS('Dot Product', 'Angle')
## Tagged by nhamblet

## DBsubject('Calculus')
## DBchapter('Vectors and the Geometry of Space')
## DBsection('The Dot Product')
## Date('5/31/2000')
## Author('Joseph Neisendorfer')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = non_zero_random(-10, 10);
$b = random(-10, 10);
$c = random(-10, 10);
$d = non_zero_random(-10, 10);
$e = random(-10, 10);
$f = random(-10, 10);

$adbecf = $a*$d + $b*$e + $c*$f;

$dist1 = sqrt(($a)**2 + ($b)**2 + ($c)**2);
$dist2 = sqrt(($d)**2 + ($e)**2 + ($f)**2);

$ans = arccos($adbecf/($dist1*$dist2));

BEGIN_TEXT
$PAR
What is the angle in radians between the vectors 
$BR \( {\bf a} \) = ($a, $b, $c)
and $BR \( {\bf b} \) = ($d, $e, $f)?

$PAR Angle: \{ ans_rule(60) \} (radians)
END_TEXT
ANS(num_cmp($ans));

ENDDOCUMENT();