A vector may change when we :

Options

A. rotate the coordinate axis changing its orientation
B. slide the vector without changing direction
C. rotate the vector
D. all of the above

Explanation

To determine when a vector may change, we need to analyze the options provided in the question. A vector is defined by both its magnitude and direction. If either of these two components changes, the vector itself changes.

Let's break down the options step by step:

1. **Rotate the coordinate axis changing its orientation**:
- When we rotate the coordinate axis, we are changing the frame of reference but not the vector itself. The vector's magnitude and direction remain the same relative to the new axis. Therefore, this option does not change the vector.
- **Conclusion**: This option is incorrect.

2. **Slide the vector without changing the direction**:
- Sliding a vector means moving it from one position to another without altering its direction or magnitude. Since both the direction and the magnitude remain unchanged, the vector itself does not change.
- **Conclusion**: This option is also incorrect.

3. **Rotate the vector**:
- When we rotate a vector, we change its direction while keeping its magnitude constant. Since the direction is one of the defining characteristics of a vector, changing the direction means the vector itself has changed.
- **Conclusion**: This option is correct.

4. **All of the above**:
- Since we have established that the first two options do not change the vector, this option cannot be correct.
- **Conclusion**: This option is incorrect.

### Final Answer:
The vector may change when we **rotate the vector**.