Parallelogram law of vectors is applicable to the addition of `:`

Options

A. Any two vectors
B. Two scalars
C. A vector and a scallar
D. Two vectors representing same physical quantity.

Answer

To solve the question regarding the applicability of the parallelogram law of vectors, we need to analyze the options provided and understand the conditions under which the parallelogram law can be applied.

### Step-by-Step Solution:

1. **Understanding the Parallelogram Law of Vectors**:
The parallelogram law states that if two vectors are represented as two adjacent sides of a parallelogram, then the resultant vector can be represented by the diagonal of the parallelogram that starts from the same point.

2. **Identifying the Nature of Vectors**:
Vectors are quantities that have both magnitude and direction. For the parallelogram law to apply, the vectors being added must represent the same physical quantity.

3. **Analyzing the Options**:
- **Option 1: Any two vectors**: This is incorrect because not all vectors can be added using the parallelogram law unless they represent the same physical quantity.
- **Option 2: Two scalars**: This is incorrect because scalars do not have direction and cannot be added using the parallelogram law.
- **Option 3: A vector and a scalar**: This is incorrect because a vector and a scalar cannot be added together in any vector addition method.
- **Option 4: Two vectors representing the same physical quantity**: This is correct because the parallelogram law is specifically designed for adding vectors that represent the same physical quantity (e.g., two forces, two velocities).

4. **Conclusion**:
The correct answer is that the parallelogram law of vectors is applicable to the addition of **two vectors representing the same physical quantity**.

### Final Answer:
The parallelogram law of vectors is applicable to the addition of **two vectors representing the same physical quantity**.