I am going to purchase DJI care for the Phantom 3.  Would I use the craft serial number and camera serial number on box to enter for purchase of the DJI care.

The DJI Care  for the Phantom 3 is available for the Pro/Adv/Std and requires both the aircraft and gimbal serial numbers. While the numbers on your box and the actual components should be the same, the DJI Care FAQ #13 shows customers verifying the numbers on the components themselves (scroll down to the FAQ # 13).
If your P3 has been activated for more than 48 hours, take a look at the verification requirements found here -> DJI_Care Customer Verification Upload requirements and documented in this PDF document.

DJI Care SN

Daroga Posted at 2016-12-14 23:30
The DJI Care  for the Phantom 3 is available for the Pro/Adv/Std and requires both the aircraft and gimbal serial numbers. While the numbers on your box and the actual components should be the same, the DJI Care FAQ #13 shows customers verifying the numbers on the components themselves (scroll down to the FAQ # 13).
If you P3 has been activated for more than 48 hours, take a look at the verification requirements found here -> DJI_Care Customer Verification Upload requirements and documented in this PDF document.

Thank you very much for posting.