Final answer:
To close an unresponsive application, the command line option taskkill should be used. It terminates tasks by their process ID or name without affecting other system processes.
Step-by-step explanation:
The command line option to only close an unresponsive application causing system instability is taskkill. This command is used in Windows to terminate tasks by process id (PID) or image name. An example of using this command is taskkill /IM application.exe, which would close the application named 'application.exe'. It's important not to confuse taskkill with commands like shutdown, which shuts down or restarts the entire system, or chkdsk, which checks the disk for errors. The tasklist command can be used prior to taskkill to view a list of all running tasks and their PIDs.