The pressure intensity at a point in a fluid is the same in all directions only when the fluid has no relative motion between adjacent fluid layers. This is based on the principle of fluid statics, which states that a fluid at rest will exert equal pressure on all surfaces in contact with it. Let us understand this in detail:

Principle of Fluid Statics:
The principle of fluid statics states that a fluid at rest will exert equal pressure on all surfaces in contact with it. This is because the pressure at any point in a fluid is determined by the weight of the fluid above it, and this weight is transmitted equally in all directions. Therefore, the pressure at any point in a fluid is the same in all directions.

Explanation of the correct option:
Option (c) states that the pressure intensity at a point in a fluid is the same in all directions only when the fluid has no relative motion between adjacent fluid layers. This is because if there is relative motion between adjacent fluid layers, it will create shear stresses, which will result in a pressure gradient in the fluid. This pressure gradient will cause the pressure intensity to be different in different directions, violating the principle of fluid statics.

Importance of fluid statics in engineering:
Fluid statics is an important concept in engineering, especially in the design of hydraulic systems. Understanding the principle of fluid statics is essential in determining the pressure distribution in a fluid and designing systems that can withstand these pressures. This principle is also important in the design of dams, reservoirs, and other structures that interact with fluids.

Conclusion:
In conclusion, the pressure intensity at a point in a fluid is the same in all directions only when the fluid has no relative motion between adjacent fluid layers. This principle is essential in understanding the behavior of fluids at rest and is important in the design of hydraulic systems and other structures that interact with fluids.