Imagine a Cartesian coordinate system whose origin is associated with two unit vectors, ê and â, in a 2D-space. Now, let 0.5 cm be the unit of length in this coordinate system.
The magnitude of a unit vector is, by definition, 1; Does this mean that the magnitude of one of our unit vectors is 1 unit of length? Or, in other words, does this mean that $\left | â \right |$ = $\left | ê \right |$ = 0.5cm?