(A): The direction of velocity vector remains unchanged though the coordinate system is changed
(R) : The direction of real vector is independent of coordinate system

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. (A) is false but (R) is true

Answer

To solve the question, we need to analyze the statements given and determine their validity based on the principles of physics.

### Step-by-Step Solution:

1. **Understanding the Statements**:
- Statement (A): "The direction of the velocity vector remains unchanged though the coordinate system is changed."
- Statement (R): "The direction of a real vector is independent of the coordinate system."

2. **Analyzing Statement (A)**:
- The velocity vector is a physical quantity that has both magnitude and direction. When we change the coordinate system (for example, from Cartesian to polar coordinates), the representation of the vector may change, but its direction in space does not.
- Therefore, Statement (A) is **True**.

3. **Analyzing Statement (R)**:
- A real vector, such as velocity, is defined by its direction and magnitude. The direction of a real vector is indeed independent of the coordinate system used to describe it. This means that regardless of how we choose to represent the vector (different axes or units), its inherent direction in the physical space remains the same.
- Therefore, Statement (R) is also **True**.

4. **Conclusion**:
- Since both statements (A) and (R) are true, and (R) provides a valid explanation for (A), we conclude that both statements are correct.

### Final Answer:
Both (A) and (R) are true, and (R) is the correct explanation for (A).

---