A typical ranch is going to have ceiling joists running front to back and joined in the middle. They will usually rest on bearing walls running the length of the house and on headers where there are openings in that wall. Not usually a "beam" per say in the attic. Is the wall you wish to take out, one side of a hallway? That would account for the 3 feet to one side and running parallel to the main wall.
You would need to see if the joists overlap on the bearing wall, determine your joist width (2x6)and the free span of the joists with the wall removed. A code book and some knowledge of reading it would tell you the allowable span of those joists with the load involved. get a pro if there is any doubt in your mind.

don92 thanks for the feedback...the wall that we wish to open up is on one side of the hallway - in fact it's the only wall in that area as the living room is open. 3 feet opposite of the wall is where the main load is carried (middle) and indicated as load bearing on blueprints. 4 columns (middle) are directly above support posts in basement where as wall section (to be removed) is over poured concrete basement wall. Doing much more research before proceeding.

As a practical matter, it is time to call a structural engineer. For a couple hundred bucks, you'll get the answers to all your questions. Also, if you are pulling permits, you'll likely be required to have his stamp of approval anyway.

BTW - blueprints are great provided the builder followed them to a T.

Also, headers are a poor indicator of loadbearing. The cost of a little extra lumber is often much less than the cost of employing someone who knows how to properly size a header.