Resolving vectors into a unit vector

[jmc]

Homework Statement

electric field polarization for a given antenna is expressed as:
E_i = (a_x + a_y) E (r, theta, phi)

The unit vector along the antenna polarization is found as u_a = 1/Sqrt(2) (a_x + a_y)2. Question
Where/how is the 1/Sqrt(2) found to resolve those other 2 vectors into a unit vector? Is there a formula or is it some kind of vector addition?
What if there was a factor of 2 added to a_y in the original equation - how would it change that unit vector result?

Thank you

 

[Orodruin]

A unit vector is defined to have length one. Given any vector $\vec v$ it can be multiplied with $N = \frac{1}{\sqrt{\vec v^2}}$ to give a vector $\frac{\vec v}{\sqrt{\vec v^2}}$ which is of unit length.