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A vector is not changed if...

A vector is not changed if

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

Text Solution

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The correct Answer is:
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.
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