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I don't know what you mean by normalizing the vectors.
Normalizing a vector is simply scaling the vector so, that it has length 1. You do this by dividing every component of the vector (x, y, z) with the magnitude or length of the vector ([math]\sqrt{x^2 + y^2 + z^2}[/math])
Normalizing a vector makes a lot of math a lot easier, since you can then use it as direction vector for many purposes.
For example, if you want to know how much of your velocity is in direction of an engine inlet, you just do a scalar product of the air velocity vector with the engine inlet direction vector. Also, if you have two such vectors, which are perpendicular, you can use them for defining a projection matrix - orbiter does that with the docking ports for example.
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