The pressure in a liquid is equal at two points in the same...

The variation of pressure in a fluid accelerating with an acceleration $\vec{a}$ is given by $\nabla P = \rho(\vec{g} - \vec{a}) = \rho \vec{g}_{\text{eff}}$.

For the pressure to be equal at two points in the same horizontal plane, the effective gravity $\vec{g}_{\text{eff}}$ must be purely vertical, meaning it should have no horizontal component.

In the case of an elevator accelerating upward, the acceleration $\vec{a}$ is vertical. Therefore, $\vec{g}_{\text{eff}} = \vec{g} - \vec{a}$ is also purely vertical. The horizontal pressure gradient is zero, and the pressure is equal at all points in the same horizontal plane.

In the case of a car accelerating horizontally, the acceleration $\vec{a}$ has a horizontal component. Thus, $\vec{g}_{\text{eff}}$ has a horizontal component, leading to a non-zero horizontal pressure gradient. The pressure will not be equal at two points in the same horizontal plane.

Therefore, the statement is valid only for the elevator.