You could create an index (=hash lookup table) by the first field of 'large'.  Then loop over @list and check if the key exists in the lookup table.

Something like

my %index;
while (<DATA>) {   # your $large
    my ($f1) = split;
    $index{$f1} .= $_;
}

my @list = qw(foo r2c1 bar r3c1);
for (@list) {
    print $index{$_} if exists $index{$_};
}

__DATA__
r1c1 r1c2 r1c3
r2c1 r2c2 r2c3
r3c1 r3c2 r3c3
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