The change ina vector may occur due to

Options

A. Rotation of frame of reference
B. Translation of frame of eference
C. Rotation of vector
D. Both (1)/ & (3)

Answer

To solve the question regarding the change in a vector, we will analyze each option provided and determine which one correctly describes how a vector can change.

### Step-by-Step Solution:

1. **Understanding the Question**:
The question asks about the conditions under which a vector can change. A vector is defined by its magnitude and direction, so any change in either of these will result in a change in the vector.

2. **Analyzing Option 1 - Rotation of Frame of Reference**:
- When we rotate the frame of reference, the vector itself does not change. For example, if we have a vector OA making an angle of 45 degrees with the x-axis and we rotate the frame by 15 degrees, the vector OA remains at 45 degrees relative to the new frame. Therefore, this option is incorrect.

**Hint**: Consider how the vector's position changes relative to the axes when the frame is rotated.

3. **Analyzing Option 2 - Translation of Frame of Reference**:
- Translating the frame of reference means moving the entire coordinate system without changing its orientation. In this case, the vector's direction and magnitude remain unchanged. Thus, this option is also incorrect.

**Hint**: Think about whether moving the origin of the coordinate system affects the vector's properties.

4. **Analyzing Option 3 - Rotation of Vector**:
- If the vector itself is rotated, then its direction changes. For instance, if vector OA is rotated by 15 degrees, its new angle with respect to the x-axis becomes 60 degrees. This clearly indicates that the vector has changed due to its own rotation. Hence, this option is correct.

**Hint**: Visualize how the vector's direction changes when you rotate it around its tail.

5. **Analyzing Option 4 - Both 1 and 3 are Correct**:
- Since we have established that option 1 is incorrect and option 3 is correct, this option cannot be true.

### Conclusion:
The only correct answer is option 3: **Rotation of vector** is the condition under which a vector can change.

### Final Answer:
The change in a vector may occur due to **rotation of vector** (Option 3).