[deutdeut]

In drawing the 3-D structure of BF3, I know it's trigonal planar. But I see in some books that the 3 bonds are in straight line, while in another book, one bond is straight-lined, one is into paper and the other in out of paper. Which is correct? And what's the difference between the use of straight line to represent bonds or using into or out of page symbols?

[english]

Both are correct.  With straight lines only, this means that you are looking directly at the molecule, all bonds in the same plane.  This is synonymous to holding your hand in front of you, palm facing you.

When one bond is a solid wedge and the other a dashed wedge, this means that you are looking at it from the side.  This would be like taking your palm from the previous analogy and turning it so your thumb is facing towards you and your pinky is away from you.

[deutdeut]

So are there any generalizations stating when we should use which kind of representations?

[english]

So are there any generalizations stating when we should use which kind of representations?

Either way is fine.

[alphahydroxy]

The choice of representation of this sort only really becomes relevant when dealing with stereochemistry of a compound, or some other properties which rely on a  description of the 3-dimensional structure.

So, if you want to make a point about the 3D structure, draw the 3D structure!