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A vector is not changed if...

A vector is not changed if

A

It is displaced parallel to itself.

B

it is rotated through an arbitrary angle.

C

it is cross-multiplied by a unit vector.

D

it is multiplied by an arbitrary scalar.

Text Solution

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The correct Answer is:
To solve the question "A vector is not changed if," we need to analyze each of the provided options to determine which one does not alter the vector. ### Step-by-Step Solution: 1. **Understanding Vector Properties**: - A vector is defined by its magnitude and direction. Any operation that changes either of these will change the vector. 2. **Analyzing Option 1**: "Displaced parallel to itself" - If a vector is displaced parallel to itself, it means it is moved without changing its direction or magnitude. - Example: If vector **A** is moved from point (x1, y1) to (x1 + d, y1) while maintaining the same direction, it remains the same vector. - **Conclusion**: This option does not change the vector. 3. **Analyzing Option 2**: "Rotated with an arbitrary angle" - Rotating a vector changes its direction. - Example: If vector **A** is rotated by 30 degrees, it points in a different direction. - **Conclusion**: This option changes the vector. 4. **Analyzing Option 3**: "Cross multiplied by a unit vector" - Cross multiplying a vector with a unit vector results in a new vector that is perpendicular to both original vectors. - Example: If vector **A** is crossed with a unit vector **k**, the resulting vector is different in direction. - **Conclusion**: This option changes the vector. 5. **Analyzing Option 4**: "Multiplied by an arbitrary scalar" - Multiplying a vector by a scalar changes its magnitude. - Example: If vector **A** is multiplied by 5, its magnitude increases, and it points in the same direction but is a different vector. - **Conclusion**: This option changes the vector. ### Final Conclusion: The only option that does not change the vector is **Option 1: "Displaced parallel to itself."**
To solve the question "A vector is not changed if," we need to analyze each of the provided options to determine which one does not alter the vector. ### Step-by-Step Solution: 1. **Understanding Vector Properties**: - A vector is defined by its magnitude and direction. Any operation that changes either of these will change the vector. 2. **Analyzing Option 1**: "Displaced parallel to itself" ...
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