Find the intersection point of a plane and ray
Perl, 107 bytes

Tested for all test cases (i.e. not tested at all)
Run with each input number on its own line on STDIN

perl -M5.010 plane.pl
0
1
0
0
0
1
3
3
1
0
0
1
^D


plane.pl:

#!/usr/bin/perl
$$_=&lt;&gt;for a..l;say$a+($t=($j*($g-$a)+$k*($h-$b)+$l*($i-$c))/($j*$d+$k*$e+$l*$f))*$d,$",$b+$t*$e,$",$c+$t*$f


This kind of problem is absolutely not a good match for perlgolf. Perl lacks vector operations and uses too many $s