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

[sugz]

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.

 

[DelcrossA]

How would you express the unit vector going from each Q to point P?

 

[sugz]

How would you express the unit vector going from each Q to point P?

it would be E=[kQ/d^2]i

 

[DelcrossA]

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.

 

[sugz]

It would be E=[kQ/2d^2](-cos45i+sin45j)