Resolving vectors into a unit vector

  • Thread starter jmc
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  • #1
jmc
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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
 

Answers and Replies

  • #2
Orodruin
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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.
 

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