What are the units of lexicon?

simply units....

The SI unit would be Newtons or a capital N

It is a derived unit. It measure distance traveled per unit of time. For example meter per second or m/s. Speed or velocity as it is sometimes called is derived from the units for distance and time.

The Joule is the unit of energy in the SI system. The most fundamental definition of the Joule is the energy (or work done) in moving 1 meter against a force of 1 Newton.

No it doesn't. A unit vector indicates direction only. The length of the orthogonal components are RELATIVE to the absolute length of the vector, thus cannot have a unit. For instance, let X'=X/x...