# Forces on symmetrical electrostatic charges

## Homework Statement

3 point charges L(-b, b) M(b, b) & N(0, 0) have charges Q, -3Q & Q.
I need to find the force on the charge at the origin.

## Homework Equations

Coulomb's Law important, here. F = 1/4∏0 q^2/r^2 r(hat)
z-component no existent (from coordinates given)
x- & y-components to be found

Now, I'm finding it difficult to see thew wood from the trees with this relatively simple thing. I'm trying to find the x- & y- bits of force between the charges 1 & 2 to the charge at the origin for each charge.

## The Attempt at a Solution

Now, F = 1/4∏ε0 ((Q(2b*-cos45)*Q)/(2cos45)) - (-3Q(2b*cos45)/(2cos45)
Then factor out the Q^2/r^2 terms.
I would like it in the form F=1/4∏ε0 (Q^2/r^2) (!!ex - !!ey) but am finding the (!!ex - !!ey) bit difficult to get due to the trig bits I think.

I'm sure this is wrong, but is the main stumbling block.
If I can get this then magnitude of force & direction of unit vector will be easy.

$$F = k \frac{Q_1 Q_2}{r^2} ~~~~~~~\text{where}~~~~k = \frac{1}{4 \pi \epsilon_o}$$