Q: Why is There No AirDrop on my iPad 3rd Generation?

Because that is the way that Apple designed AirDrop in iOS 7 to work as stated at the bottom of the website that I referenced below.

AirDrop is available on iPhone 5 or later, iPad (4th generation), iPad mini, and iPod touch (5th generation) and requires an iCloud account.

http://www.apple.com/ios/whats-new/