Calculating the Electric Field Strength at a certain point with multiple point charge

fisixC

1. The problem statement, all variables and given/known data

Attached picture with the given variables and questions stated.

2. Relevant equations

E = kq / (r^2)

3. The attempt at a solution

I've taken found the linear electric field magnitudes in relationship to the point

q1 = 3.37e-9
q2 = 6.74e-9
q3 = 3.92e-9

r1 = .647m
r2 = 1.941m

E1 = (k*(q1))/(r1) = 72.3540189055
E2 = (k*(q2))/(r2) = 16.0789708679

I am having difficulty figuring out how to calculate the third vector into the total, any thoughts?

Attached Thumbnails

 

SammyS

Hi fisixC.

Pythagoras tells us that:
r₃² = r₁² + r₂²

The y-component of r₃ is |r₁|/|r₃| .

The x-component of r₃ is ‒|r₂|/|r₃| .

It may also help to notice that 1.941 = 3×0.647 .

Therefore,

|r₁|/|r₃| = |r₁|/√(10)

|r₂|/|r₃| = 3|r₁|/√(10)