By definition pressure is the perpendicular force applied to a unit area. So it has a direction which is perpendicular to the area. So it should be a vector. But I did sone googling and found out that it is a scalar quantity. So it would really be helpful if someone could show me how pressure is scalar with some mathematical derivation.
Answer
Pressure is proportionality factor. Area is the one that gives you direction. You have to recall that pressure is defined everywhere in the bulk volume, not just at the surface. A volume of gas has pressure defined everywhere. And the force direction is determined by you - by the way you orient your surface that you put into the gas.
$$\vec{F}=p\vec{A}$$ Here you see that the area is the vector.
Quoting wikipedia:
It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.
I should clarify, that this calculates the force caused by the pressure, so it GIVES you the force perpendicular to the area, given the area vector. It's the defining equation and the only one that captures what pressure actually does, so it's always true, but needs to be understood as a formula for calculating the force from pressure.
If $\vec{F}$ is just caused by the pressure, it can't be anything else but perpendicular to the area, otherwise you have other forces present in the system, or the liquid is not isotropic. That being said, assuming that $\vec{F}$ is only caused by the pressure, you could calculate $p$ by taking absolute values:
$$p=\frac{|F|}{|A|}$$
Mathematically, you transformed a vector equation into a scalar equation assuming parallel vectors, so now you're not allowed to put in anything, but only lengths (or projections - similar argument) of F and A that are guaranteed to have been parallel, otherwise you get nonsense. You also lose the sign of pressure (for gasses, it can't happen, but for elastic solids or liquids, it can "pull" due to intermolecular forces).
However, strictly speaking, pressure is a tensor, but for gasses, it's isotropic, so it acts as a scalar. Without going into details what a tensor is, imagine above that in $p\vec{A}$, $p$ can also transform the direction, not just the magnitude of $\vec{A}$, so the force does not have to point perpendicularly. This is true in elastic solids, where you can transmit sideways forces to the surface, and in viscous flowing liquids, where the viscous force is also just a stress (generalized pressure) transmitted to the surface. In this situation, $p$ has $6$ independent components, so you cannot measure it just by measuring a force on a single surface. You'd need to measure all components of force on 3 surfaces placed in different orientations. Only in gasses, you can rely on the force having the same magnitude no matter the orientation.
Further reading:
https://en.wikipedia.org/wiki/Cauchy_stress_tensor
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