You can treat W like a scale factor, although it works the opposite way:

[2,2,2,2] is actually [1,1,1].

The use of 4 coords rather than 3 makes a lot of the maths easier, which is the main reason for using it.

Generally it''s best to keep x,y,z,w coords in x,y,z,1 format .. i.e. divide all by ''w'' (hence 2,2,2,2 being converted to 1,1,1,1)

Usually referred to as ''homogenous'' coordinates (meaing in this case all having w=1)

I read quite a good (short) explanation of it recently, somewhere, but can''t remember where .. probably either in the Red Book or OpenGL Game Programming.

using 1x4 vectors means that you can modify them with 4x4 matrices (meaning that you can easily perform translates+scales+rotates in ways which would be far more complex if u had to only use 3x3 matrices).

TBH, you probably don''t care .. just keep w=1