Three charges are fixed to an xy coordinate system. A charge of +16C is on the y axis at y = +3.1 m. A charge of -16C is at the origin. Lastly, a charge of +55C is on the x axis at x = +3.1 m. Determine (a) the magnitude and (b) direction of the net electrostatic force on the charge at x = +3.1 m. Specify the direction as a positive angle relative to the +x axis.

I figured out how to set up the problem in general, but i keep getting the wrong answer. Please help!
So this is what I have gotten so far. I don't understand how to get the direction at all.

(9x10^-9)* (((18x10^-6)(55x10^-6))/ 3.1^2+3.1^2= 0.46357

q1 = 16 C, q2 =-16 C, q3 =55 C.

Distance between q1 and q3 r1= 3.1•√2 m.
Distance berween q2 and q3 r2 =3.1 m

Make the drawing: two forces acting on q3:
force F1 - along the “q1-q3” line - repulsion,
force F2 - along the “q2-q3” line - attraction.
F1 =k•q1•q3/r1² =9•10^9•16•55/(3.1•√2)²=4.12•10^11 N.
F2 =k•q2•q3/r1² =9•10^9•16•55/(3.1•2)²=8.24•10^11 N.
Net force is opposite the angle 45º according to the Cosine Law:
F12=sqrt(F1² +F2²-2•F1•F2•cos45 º) = 6.1•1011 N.
Two other angles in the “force triangle” we’ll find using Sine Law:
6.1•10^11/sin45=4.12•10^11/sinα,
sinα =0.478, α =28.5º
6.1•10^11/sin45=8.24•10^11/sinβ,
sinβ =0.94, β =70.2 º,
α+β =28.5+70.2=98.7 º - this is the angle that F12 makes with x-axis (below its positive direction)

To find the net electrostatic force on the charge at x = +3.1 m, you need to consider the contributions from each of the three charges. Here's the step-by-step process:

1. Calculate the electric force between the charge at x = +3.1 m and the charge at the origin:
- Charge at x = +3.1 m: +55 C
- Charge at the origin: -16 C
Using Coulomb's Law, the magnitude of the electric force (F1) between these two charges is given by:
F1 = (k * |q1| * |q2|) / r^2
where k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Plugging in the values:
F1 = (9 x 10^9 N m^2/C^2) * ((55 x 10^-6 C) * (16 x 10^-6 C)) / (3.1 m)^2
F1 ≈ 5.95 N (rounded to two decimal places)

2. Calculate the electric force between the charge at x = +3.1 m and the charge on the y-axis:
- Charge at x = +3.1 m: +55 C
- Charge on the y-axis: +16 C
Using Coulomb's Law, the magnitude of the electric force (F2) between these two charges is given by:
F2 = (k * |q1| * |q2|) / r^2
In this case, since the two charges have the same sign (+), the force is repulsive.
Plugging in the values:
F2 = (9 x 10^9 N m^2/C^2) * ((55 x 10^-6 C) * (16 x 10^-6 C)) / (3.1 m)^2
F2 ≈ 5.95 N (rounded to two decimal places)

3. Calculate the vector sum of F1 and F2:
To find the net electrostatic force, you need to sum the vectors F1 and F2 using vector addition.
F_net = F1 + F2
F_net = √(F1^2 + F2^2)
F_net ≈ √((5.95 N)^2 + (5.95 N)^2)
F_net ≈ √(70.7025 N^2 + 70.7025 N^2)
F_net ≈ √(141.405 N^2)
F_net ≈ 11.90 N (rounded to two decimal places)

Now, to determine the direction of the net electrostatic force relative to the +x axis, you can use trigonometry. We have two equal forces F1 and F2 acting along the positive x-axis and y-axis, respectively, at angles of 45 degrees with respect to the positive x-axis.

4. Calculate the direction of the net electrostatic force:
Use the following formula to find the direction of the net electrostatic force (θ):
θ = tan^(-1)((sum of the y-components)/(sum of the x-components))
where the sum of the y-components is F2 and the sum of the x-components is F1.
Plugging in the values:
θ = tan^(-1)((5.95 N)/(5.95 N))
θ = tan^(-1)(1)
θ ≈ 45°

Therefore, the magnitude of the net electrostatic force on the charge at x = +3.1 m is approximately 11.90 N, and the direction is 45° relative to the +x axis.

To find the net electrostatic force on the charge at x = +3.1 m, we need to consider the electric forces exerted by each of the other charges. Let's break it down step by step:

Step 1: Calculate the electric force between the charge at x = +3.1 m and the charge at the origin.

Given:
Charge at x = +3.1 m: +55 C
Charge at the origin: -16 C

Electric force between two charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2

where F is the force, k is the electrostatic constant (9 * 10^9 N*m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.

Substituting the values:
F1 = (9 * 10^9 * |55 * 16|) / (3.1)^2

Step 2: Calculate the electric force between the charge at x = +3.1 m and the charge on the y-axis.

Given:
Charge at x = +3.1 m: +55 C
Charge on the y-axis at y = +3.1 m: +16 C

Using Coulomb's Law:
F = (k * |q1 * q2|) / r^2

Substituting the values:
F2 = (9 * 10^9 * |55 * 16|) / (3.1)^2

Step 3: Find the resultant force by summing up the electric forces in vector form.

The magnitude of the resultant force can be found using the Pythagorean theorem:
Resultant force = sqrt(F1^2 + F2^2)

Step 4: Find the direction of the resultant force.

The direction of the resultant force can be calculated using trigonometry. We need to find the angle created by the resultant force with the +x axis.

Angle = arctan(F2 / F1)

Substitute the obtained values into the equation to get the magnitude and direction of the net electrostatic force on the charge at x = +3.1 m.