Explain why:
$(a)$ The blood pressure in humans is greater at the feet than at the brain.
$(b)$ Atmospheric pressure at a height of about $6 \; km$ decreases to nearly half of its value at sea level,though the height of the atmosphere is more than $100 \; km$.
$(c)$ Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

(N/A) The pressure of a liquid is given by the relation $P = h \rho g$,where $P$ is pressure,$h$ is the height of the liquid column,$\rho$ is the density of the liquid,and $g$ is the acceleration due to gravity.
$(a)$ Pressure is directly proportional to the height of the fluid column $(P \propto h)$. In the human body,the height of the blood column above the feet is greater than the height of the blood column above the brain. Therefore,the blood pressure at the feet is higher than at the brain.
$(b)$ The density of air is maximum near sea level and decreases exponentially with altitude. At a height of about $6 \; km$,the density of air drops to nearly half of its value at sea level. Since atmospheric pressure is directly related to the density of the air column above,it also decreases to nearly half of its sea-level value at this height.
$(c)$ Pressure is defined as the normal force per unit area. When force is applied to a fluid,the pressure is transmitted equally in all directions (Pascal's Law). Since it does not have a specific direction associated with it,hydrostatic pressure is considered a scalar quantity.