Reciprocity theorem is a fundamental principle in the field of structural analysis, which states that the influence of a force applied to one structure on another structure is the same as the influence of the same force applied to the second structure on the first structure. In other words, it establishes a relationship between the forces applied on two different structures.

The reciprocity theorem can be mathematically expressed in terms of the forces and displacements as follows:

a) F12 = F21
b) A1F12 = A2F21
c) A1F21 = A2F12
d) A2F21 = A1F12

Among these options, option 'B' is correct, which states A1F12 = A2F21. This equation represents the relationship between the forces and the areas of the two structures.

Let's break down the explanation of option 'B' in detail:

1. A1F12:
- A1 represents the area of the first structure.
- F12 represents the force applied on the first structure.

2. A2F21:
- A2 represents the area of the second structure.
- F21 represents the force applied on the second structure.

According to the reciprocity theorem, the product of the area of one structure and the force applied on the other structure is equal to the product of the area of the other structure and the force applied on the first structure.

This can be understood by considering two interconnected structures, where a force is applied on one structure and the effect of this force is observed on the other structure. The reciprocity theorem states that the force experienced by the second structure due to the applied force on the first structure is the same as the force experienced by the first structure due to the applied force on the second structure.

This principle is widely used in various fields of engineering, such as structural analysis, acoustics, and electromagnetic theory. It allows engineers to analyze and predict the behavior of structures and systems by considering the reciprocal effects of forces and displacements.

In conclusion, option 'B' in the reciprocity theorem states that the product of the area of one structure and the force applied on the other structure is equal to the product of the area of the other structure and the force applied on the first structure. This principle is essential in understanding the reciprocal effects between interconnected structures.