Consider the charges q, q and -q placed at the vertices of an equilateral triangle, as shown in the figure. What is the force on charge -q ?
 

The force that acts on each of the three charges kept at the given equilateral triangle is
Now, the force is given by
$\mathrm{F}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}^2}{{\mathrm{l}}^2}$
and therefore the force on the charge -q is given by
$$\begin{gathered} {\mathrm{F}}_{-\mathrm{q}}=\sqrt{{{\mathrm{F}}^2}_{ }+{{\mathrm{F}}^2}_{ }+2\mathrm{FF} \cos {60}^{\mathrm{o}}}=\sqrt{3}\mathrm{F} \\ \Rightarrow \sqrt{3}\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}^2}{{\mathrm{l}}^2}\right)=\left(\frac{\sqrt{3}}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}^2}{{\mathrm{l}}^2}\right) \end{gathered}$$