In order to hard reset a Samsung Vibrant, you should perform the following steps.

Remember! Hard reset will delete all the data on your device; pictures, contacts, messages, apps and more.
Samsung Vibrant device will be brought back to the default configuration of a brand new device.

1. Turn off the phone by holding the Power button.

2. Press'n'hold these three buttons simultaneously: Volume Up and Down, Power. Let go of them when the Samsung logo appears.

3. A new menu should now open. From it, select the Wipe data/factory reset option.  To do so, use Volume buttons to scroll the menu and Power button to choose the option.

4. Now select, in the same way as above, Yes and Reboot system now.

5. Done!