JD_Toims - 7:36 pm on Aug 27, 2013 (gmt 0)
As Lucy24 said, it looks like you're working in the httpd.conf not the .htaccess. If that's not the case you'll need to remove the / from the left side of the rule since it's not present in the .htaccess, otherwise it looks like some of what you've tried should work, which makes me wonder if you rebooted the server and emptied your cache prior to testing?
RewriteRule ^/tece(.*)$ http://www.example.com/our_business/plastics/pvc-vcm/$1 [R=301,L]
I made a couple of adjustments to one of your test rules, but what you had appears like it should have worked to redirect even though there were a couple of details missing.
I added tece to match the correct directory, the $1 back-reference to the right side for a page-to-page redirect and also the L flag, which should always be used unless you know exactly why you don't want it.