Why does the magnitude of unit vector change equal the angle change in polar coordinates?

[Azorspace]

Homework Statement

we have this diagram were it says that the change in the unit vector der equals in magnitude the change in the angle between the two unit vectors er. Could someone explain me why is this?

I include the diagram named Polar coordinates.

 

[JoAuSc]

I don't think de_r is a unit vector. It is the difference between two unit vectors, but it itself is not a unit vector.

 

[borgwal]

He doesn't say that de_r is a unit vector, it's the *change* in a unit vector.

But to answer the original question: yes, if you consider |e_1-e_2|^2 and use that e_1 is only a little (infinitesimally) different from e_2, e_1=e_2+\delta e, then you'll find what you need by comparing the answer to e_1\cdot e_2, and using how the angle between two vectors relates to the angle between the vectors, and Taylor expanding the cosine for small angles.