The law of parallelogram of vector addition is a mathematical principle that describes how two vectors can be added together to find their resultant vector. It is based on the geometrical properties of parallelograms.

**Statement of the Law:**
The law of parallelogram of vector addition states that if two vectors are represented by the adjacent sides of a parallelogram, then the diagonal of the parallelogram passing through their point of intersection represents the resultant vector.

**Explanation:**
To understand the law of parallelogram of vector addition, consider two vectors A and B. These vectors can be represented by arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.

1. **Constructing a Parallelogram:**
- Draw vector A as an arrow starting from a point O.
- Draw vector B as an arrow starting from the same point O, but in a different direction.
- Complete the parallelogram by drawing lines parallel to the vectors A and B, starting from the endpoints of the vectors.
- The diagonal of the parallelogram passing through the point O represents the resultant vector.

2. **Finding the Resultant Vector:**
- Measure the length of the diagonal using a ruler. This length represents the magnitude of the resultant vector.
- Determine the direction of the resultant vector by drawing an arrow along the diagonal. The direction of the arrow indicates the direction of the resultant vector.

3. **Properties of the Resultant Vector:**
- The resultant vector is the vector sum of the two original vectors A and B.
- The magnitude of the resultant vector is equal to the length of the diagonal of the parallelogram.
- The direction of the resultant vector is given by the direction of the diagonal of the parallelogram.

4. **Vector Addition Using Components:**
- The law of parallelogram of vector addition can also be applied using vector components.
- Break down the vectors A and B into their x and y components.
- Add the corresponding components of the vectors to obtain the x and y components of the resultant vector.
- Combine the x and y components to find the magnitude and direction of the resultant vector.

In conclusion, the law of parallelogram of vector addition provides a graphical and algebraic method to find the resultant vector by using the properties of parallelograms. It is a fundamental concept in vector algebra and is widely used in various fields such as physics, engineering, and mathematics.