OS: Windows 2008 Server R2
Oracle Client: 11.2
Many Thanks
A simple way to find this out in Windows is to run SQLPlus from your Oracle homes's bin directory and then check Task Manager. If it is a 32-bit version of SQLPlus, you'll see a process on the Processes tab that looks like this:
sqlplus.exe *32
If it is 64-bit, the process will look like this:
sqlplus.exe