Three vessels A , B , and C have identical base areas. Vessel A is...

The pressure $P$ exerted by a liquid at a depth $h$ is given by $P = \rho g h$.

Since all three vessels are filled with the same liquid to the same height $h$, the pressure at the base of each vessel is identical.

The force exerted by the liquid on the base is given by $F = P \times A$, where $A$ is the base area.

As the base areas of all three vessels are identical, the force exerted by the liquid on the base is exactly the same for all three vessels, regardless of their shapes or the total volume of liquid they contain. Thus, $F_A = F_B = F_C$.

Answer: $F_A = F_B = F_C$