State and prove Pascal's law.

(N/A) Law: "The pressure in a fluid at rest is the same at all points in all directions if gravity is neglected."
Proof: Consider a small element $ABC-DEF$ in the interior of a fluid at rest, in the form of a right-angled prism. Since the element is very small, the effect of gravity can be neglected.
Let the areas of the surfaces be $A_a$ (bottom surface $BEFC$), $A_c$ (vertical surface $ABED$), and $A_b$ (inclined surface $ADFC$).
Let the forces acting perpendicular to these surfaces be $F_a$, $F_c$, and $F_b$ respectively.
From the geometry of the prism:
$A_a = A_b \cos \theta$
$A_c = A_b \sin \theta$
For the element to be in equilibrium, the net force in any direction must be zero:
Horizontal direction: $F_c = F_b \sin \theta$
Vertical direction: $F_a = F_b \cos \theta$
Since pressure $P = F/A$, we have:
$P_c = F_c / A_c = (F_b \sin \theta) / (A_b \sin \theta) = F_b / A_b = P_b$
$P_a = F_a / A_a = (F_b \cos \theta) / (A_b \cos \theta) = F_b / A_b = P_b$
Thus, $P_a = P_c = P_b$. This proves that the pressure at all points in a fluid at rest is the same.