Where Should a 30nC Charge Be Placed to Nullify Electric Field at the Origin?

[LeeroyJenkins]

Homework Statement

In free space, Q1 = 10nc at P1(0,-4,0) and Q2 = 20nC at P2(0,0,4).
a. Find E at the origin (answered)
E(r) = 5.617ay - 11.235az
b. Where should a 30nC point charge be located so E=0 at the origin? (need help)

Homework Equations

E(r) = (1/4(pi)epsilon) sum ((Qm)am/(|r-rm|^2))
formula for electric field intensity

The Attempt at a Solution

E = 0, Q3 = 30nC
E = 0 = (1/4(pi)epsilon) ( (Q1)a1/(|r-r1|^2))+ ...)
a3 = (0-x)ax + (0-y)ay + (0-z)az/ |r-r3|
x = 0
P3 = (0, y, z)

5.617ay - 11.235 az = ((Q3)a3/(|r-r3|^2))

*5.617ay - 11.235 az = Q3((0-y)ay + (0-z)az/ |r-r3|^3)
**|r-r3| = sqrt(0^2 + (0-y)^2 + (0-z)^2)
* and ** aren't enough to solve I'm missing one thing any help would be appreciated.

 

[trav]

(0, -5.62, +11.23) = (3x10^-8+12)/(4pi8.854) (0, -y, z)\(y ²+z ²) 1.5 ; -5.62 = 270 -y/(y ²+z ²) 1.5 and 11.23 = 270 -z/ (y ² + z ²); -0.5 = y/z, (y ² + 4y ²)1.5=48y, y=2.07, z = -4.14, The location is (0, 2.07, -4.14). The trick is dividing y by z!