What is the Electric Field at P(0,0,4)?

[LeeroyJenkins]

Homework Statement

Infinite unknown line charges of 5nC/m lie along the (positive and negative) x and y axes in free space. Find E at P(0,0,4)

Homework Equations

E = (pl/2(pi)(eo)p)ap
pi = 3.14...
eo - permitivity of free space 8.854 x 10^-12
pl = line charge density
ap = unit vector

The Attempt at a Solution

really just need to know how to solve for the unit vector pl then I can do the rest.
I was thinking along the lines of ap = (z-4) az/ sqrt((z-4)^2) then plug in z... not really sure. Any help would be appreciated.

The answer is 45az but how?

 

[LowlyPion]

Why the unit vector pl?

Through symmetry (You're on the z-axis) isn't the set up equivalent to just a single line charge with density 10 taken from the radius of 4?