Solving for Electric Field: q1, q2, q3 & r1, r2

[fisixC]

Homework Statement

Attached picture with the given variables and questions stated.

Homework Equations

E = kq / (r^2)

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?

 

[SammyS]

Homework Statement

Attached picture with the given variables and questions stated.

Homework Equations

E = kq / (r^2)

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?

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)