The issue with normalization is that you lose a degree of freedom - which when you're visualizing, effectively means losing a dimension. Normalized 2d vectors a

The issue with normalization is that you lose a degree of freedom - which when you're visualizing, effectively means losing a dimension. Normalized 2d vectors are really just 1d vectors; if you want to show a 2d relationship, now you have to use 3d vectors (so that you have 2 degrees of freedom again).