The right rear wheel of my ‘02 F-150 is locking up.
Is there a problem with my emergency brake?

 

Because both use some of the same parts to work, the only way to know for sure which is causing the problem, the wheel needs to be removed and the brake parts actually checked.

Grease or brake fluid getting on the friction parts can cause the wheel to lock up on brake application, so can broken brake hardware..Requires visual inspection to determine the exact cause.

 

Check my signature below. Additionally what's the 8th character of your VIN.
Also why you think there is a problem with your parking brake. Anything wrong with your red brake light?

 

What should look for?

 

Anything like grease ,oil or brake fluid on pads or brake shoes, also the parts that secure the shoes to the backing plate.

That should give you plenty to check..