Depending on the year of truck, you may not need to go in reverse. Older 4x4's had you go in reverse in order for the front hubs to disengage allowing them to free wheel. Most newer 4x4's now don't require you to go in reverse to release it anymore.
drive in reverse like 10 feet
Yes you can, in reverse!
Your 4 wheel drive may be engaged. Take out of 4 wheel drive and put it in reverse. Drive the car in reverse while turning the steering wheel all the way from one side to the other until it disengages.
Of course
Rear wheel drive --could be a bad "U" joint Could be wheel bearing Could be rear brakes not releasing completely Could be a bad tire causing a "bump" and shock absorber movement Could be a worn shock mount Could be a worn or broken spring
The emergency brake cable is probably seized and the emergency brake is not releasing.
have you tried to get your wheel realigned
If it is a front wheel drive vehicle it could be a bad CV joint. In a rear wheel drive car it could be a bad universal joint.
a blown transmission
Shift it on 2H, then "REVERSE" for about 10 to 15 Feet....
This happen to me several times, put the car in reverse (R) & drive in a circle, it will pop out, then you can turn button to 2 wheel drive. Good luck!
Check your power steering fliud, if it is low this could cause the vibration you are feeling.