07-10-2012 02:51 AM - edited 07-10-2012 02:55 AM
Yes you can activate and you can use the same Key you have used to Activate in your 64bit OS.
If you dont' have the Product Key you can Register to the Norton Account in your 64-bit OS and login with the Same e-mail address in your 32-bit OS. This will help you actiavte in 32-bit OS and you can use N360 in both the OS.
Hope this helps to fix your issue.
Please let us know if you need any help.If the issue is fixed please close the thread so that any one who have the same issue can be of help.