Java is properly installed in my Ubuntu 12.04 and the PATH variable is set in the .bashrc
file.
The command java -version
gives an expected out
You can explicitely tell your eclipse session which jdk/jre you want it to start with adding the following in your eclipse.ini
:
-vm home/..../jre/bin/javaw.exe
Install eclipse via the package manager and you shouldn't have this problem.
You've installed eclipse manually in your home directory and eclipse is trying to find a jre where it was installed, but you probably didn't download a version of eclipse that comes with its own jdk. As such it needs a little more help to work.
Like I said above, delete your current installation and install via the package manager.