Give the relation between vacuum permittivity $(\epsilon_{0})$, vacuum permeability $(\mu_{0})$, and the speed of light $(c)$.

We know that the electrostatic constant is $\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \text{ Nm}^{2}/\text{C}^{2}$ and the magnetic constant is $\frac{\mu_{0}}{4 \pi} = 10^{-7} \text{ Tm/A}$.
Multiplying these two constants:
$\mu_{0} \epsilon_{0} = \left( \frac{\mu_{0}}{4 \pi} \right) \left( 4 \pi \epsilon_{0} \right) = (10^{-7}) \left( \frac{1}{9 \times 10^{9}} \right) = \frac{1}{9 \times 10^{16}}$.
Since the speed of light in vacuum is $c = 3 \times 10^{8} \text{ m/s}$, we can write:
$\mu_{0} \epsilon_{0} = \frac{1}{(3 \times 10^{8})^{2}} = \frac{1}{c^{2}}$.
Therefore, the relation is $c = \frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}$.