Login to the server which you have the DB installed on
[bash]sqlplus /nolog #login to SQL*Plus console[/bash]
From SQL*Plus console:
[sql]conn user/pass as sysdba
var ohp varchar2(100);  –set a variable ‘ohp’
exec dbms_system.get_env(‘ORACLE_HOME’, &#58ohp) ; –call the get_env system-procedure
print ohp; –prinout the result[/sql]

You should then see an output print of the ORACLE_HOME path for the DB installed:

[sql]/u01/app/oracle/product/10.2.0/db_1[/sql]