Difference between "far" and "far away"

The library is far.

The library is far away.

I was told that far and far away are both fine and express the same meaning in the above sentences. But, I was told that only far away can be used in the following sentence (far is wrong).

On top of the mountain, I can see things far away.

*On top of the mountain, I can see things far.

Why? I haven't got a good explanation.

Far away indicates something or someone that is far from something else, and implies two points, a here, and a 'there' being referred to. Far however is more general and can be used in more cases e.g. "he went far in his studies"

Your latter example is also grammatically wrong.

On top of the mountain, I can see things far away.

On top of the mountain, I can see things needs a word here far.

e.g. that are quite but there are many other sentences that would make much more sense grammatically, and meaningfully.

I'd also suggest an additional word in the first sentence too, e.g.

I can see things that are far away.

There is also a better sentence involving far:

On top of the mountain, I can see far.