Why is Root-2 in the Denominator of the Homework Solution?

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The discussion revolves around the presence of √2 in the denominator of a physics homework solution related to electric fields. The participant seeks clarification on how to express the unit vector from charges Q to point P, particularly in a coordinate system. They note that the electric field E is calculated as E=[kQ/d^2]i for one charge and mention the need to adjust for the second charge. The correct expression for the combined electric field involves a factor of 2 in the denominator due to the geometry of the problem, specifically the angles involved. Understanding the coordinate system and the geometry is crucial for correctly applying the formulas.
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Homework Statement


Attached below

Homework Equations


E = [kq/r^2]r -------> r is the unit vector

The Attempt at a Solution


I did the same thing as the solution below, however, I do not understand why there is root-2 in the denominator. I would appreciate it if someone could explain this to me.
 

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How would you express the unit vector going from each Q to point P?
 
DelcrossA said:
How would you express the unit vector going from each Q to point P?
it would be E=[kQ/d^2]i
 
sugz said:
it would be E=[kQ/d^2]i

That's for one of the Q's. What about for the other one?

Note that it's essential to make sure you have set up a clear coordinate system for the problem.
 
It would be E=[kQ/2d^2](-cos45i+sin45j)
 
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