A vector is not changed if

Options

A. Frame of reference is translated
B. Vector is translated parallel to itself
C. Vector is rotated
D. Both (A) and (B)

Answer

To determine when a vector is not changed, we need to analyze the conditions provided in the question. A vector is defined by both its magnitude and direction. Therefore, for a vector to remain unchanged, both of these properties must remain constant.

### Step-by-Step Solution:

1. **Understanding the Vector**:
A vector has both magnitude (length) and direction. For a vector to remain unchanged, both these aspects must not vary.

2. **Analyzing Option 1: Frame of Reference is Translated**:
- When we translate the frame of reference, we are essentially moving the entire coordinate system without altering the vector itself.
- The direction and magnitude of the vector remain the same because we are just shifting our perspective.
- **Conclusion**: The vector does not change in this case.

3. **Analyzing Option 2: Vector is Translated Parallel to Itself**:
- Translating a vector parallel to itself means moving it without changing its direction.
- For example, if we move the vector up or down while keeping it parallel, its magnitude and direction remain unchanged.
- **Conclusion**: The vector does not change in this case either.

4. **Analyzing Option 3: Vector is Rotated**:
- Rotating a vector means changing its direction while keeping its magnitude the same.
- If we rotate the vector, it points in a new direction, which means it has changed.
- **Conclusion**: The vector does change in this case.

5. **Final Evaluation**:
- From the analysis, we find that options 1 and 2 do not change the vector, while option 3 does change it.
- Therefore, the correct answer is that both options 1 and 2 are correct, leading us to option 4, which states that both A and B are correct.

### Final Answer:
The vector is not changed if:
- A) The frame of reference is translated.
- B) The vector is translated parallel to itself.
- Therefore, the correct option is **4) Both A and B are correct**.