Adding yet another solution to the mix.. I assumed that new files start with VECT and that no blank lines go into output files. If a file handle like OUT below is open to one file and an open is issued to a new file, that causes an automatic close of the previous file. So the code is actually very simple. Code of course assumes that first non-blank line is a VECT line.

#!/usr/bin/perl -w
use strict;

my $num =1;
while (<DATA>)
{
   next if /^\s*$/;  #skip blank lines
   
   if (/^VECT/)
   {
      open OUT, '>', "file$num" or die "unable to open file$num $!\n";
      $num++;
   }
   
   print OUT $_;
   
}
close OUT;  #to finish the very last file in a clean way

__DATA__
VECT
1 1 1
2 2 2
3 3 3

VECT
4 4 4
5 5 5
6 6 6
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