AskPhysics

Surfaces are vector quantities so write :
P . S_vector = F_vector

If you take a small fluid element inside a fluid, the pressures on its sides are trying to compress it from all directions. But that doesn't make pressure itself a vector. The force due to the pressure on each face of the fluid element is a vector, but the pressure causing that force is just a magnitude.

If pressure were a vector, it would need a specific direction in three-dimensional space. The very fact that pressure acts equally in all directions at a point in a fluid reinforces its scalar nature.

If you're thinking about the force exerted on the walls of a container due to the pressure of the gas inside, then you're dealing with vectors. The force on a specific part of the wall has a magnitude (due to the pressure) and a direction (perpendicular to that part of the wall). But the pressure itself, which causes that force, remains scalar.

While pressure results in forces that have clear directions, the pressure itself does not have a specific direction. It is simply a measure of how much force is exerted per unit area, without specifying which direction that force is applied.