Disk Utility not opening in Mavericks
It appears that Disk Utility.app has been replaced by an incorrect version, or you are attempting to open a Disk Utility from a different installation of OS X. Make sure that you are opening Disk Utility from /Applications/Utilities and not from any other volume.

You can replace Disk Utility by re-installing OS X, which will replace all Apple apps in /Applications with new versions from the installation media.

Alternatively, you can use a Time Machine backup or other backup media to obtain a replacement copy of Disk Utility.

If you have a second computer with exactly the same version of OS X, you can copy it from that computer into the same location on the first computer. Once you have done this, boot into the Recovery HD with ⌘R and Repair Disk Permissions to ensure that the app has the proper permissions.