A vector is not changed if

Options

A. it is rotated through an aribitrary angle
B. it is multiplied by an arbitrary scalar
C. it is cross multiplied by a unit vector
D. it is slid parallel to itself

Answer

To determine when a vector is not changed, we need to analyze the options provided:

1. **Rotated through an arbitrary angle**: When a vector is rotated, its direction changes. Therefore, the vector is changed.

2. **Multiplied by an arbitrary scalar**: Multiplying a vector by a scalar changes its magnitude. Thus, the vector is changed.

3. **Cross multiplied by a unit vector**: Cross multiplication alters the direction of the vector, resulting in a different vector. Hence, the vector is changed.

4. **Slid parallel to itself**: When a vector is slid parallel to itself, both its magnitude and direction remain unchanged. Therefore, the vector is not changed.

Based on the analysis above, the correct answer is that a vector is not changed when it is **slid parallel to itself**.

### Step-by-Step Solution:
1. **Identify the nature of a vector**: A vector has both magnitude and direction.
2. **Evaluate each option**:
- **Option 1**: Rotating a vector changes its direction.
- **Option 2**: Multiplying by a scalar changes its magnitude.
- **Option 3**: Cross multiplying changes its direction.
- **Option 4**: Sliding parallel to itself keeps both magnitude and direction the same.
3. **Conclude**: The only situation where the vector remains unchanged is when it is slid parallel to itself.