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vector is not changed if...

vector is not changed if

A

it is rotated through an arbitrary 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.

Text Solution

AI Generated Solution

The correct Answer is:
To determine when a vector does not change, we need to analyze each option provided in the question. ### Step-by-Step Solution: 1. **Understanding Vector Properties**: A vector is defined by both its magnitude and direction. For a vector to remain unchanged, both these properties must stay the same. 2. **Evaluating Option 1**: - **Statement**: A vector is not changed if it is rotated through an arbitrary angle. - **Analysis**: Rotating a vector changes its direction. Since the direction of the vector changes, the vector itself is altered. - **Conclusion**: This option is incorrect. 3. **Evaluating Option 2**: - **Statement**: A vector is not changed if it is multiplied by an arbitrary scalar. - **Analysis**: Multiplying a vector by a scalar changes its magnitude. Therefore, the vector is not the same after this operation. - **Conclusion**: This option is incorrect. 4. **Evaluating Option 3**: - **Statement**: A vector is not changed if it is cross-multiplied by a unit vector. - **Analysis**: Cross-multiplying a vector with a unit vector results in a new vector that is perpendicular to both. This operation changes the direction and magnitude of the original vector. - **Conclusion**: This option is incorrect. 5. **Evaluating Option 4**: - **Statement**: A vector is not changed if it is slid parallel to itself. - **Analysis**: Sliding a vector parallel to itself means that both its magnitude and direction remain unchanged. The vector retains its original properties. - **Conclusion**: This option is correct. ### Final Answer: The vector is not changed if it is slid parallel to itself. ---
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