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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
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A vector is not changed ifa)Itis displaced parallel to itselfb)It is r...
When a vector is displaced parallel to itself, neither its magnitude nor its direction changes.
Most Upvoted Answer
A vector is not changed ifa)Itis displaced parallel to itselfb)It is r...
Understanding Vector Displacement
Vectors are mathematical entities characterized by both magnitude and direction. The options provided examine different transformations applied to a vector to determine if its essence remains unchanged.
Displacement Parallel to Itself
- When a vector is displaced parallel to its original direction, it retains its characteristics.
- The magnitude and direction remain constant, just shifted in space.
- This transformation does not alter the vector's identity, making it unchanged.
Rotation Through an Arbitrary Angle
- Rotating a vector alters its direction while maintaining the same magnitude.
- This transformation changes the vector's components, hence it is not unchanged.
Cross-Multiplication by a Unit Vector
- Cross-multiplying a vector by a unit vector results in a new vector that is perpendicular to both.
- This operation changes the vector's direction, hence it is not unchanged.
Multiplication by an Arbitrary Scalar
- Multiplying a vector by a scalar changes its magnitude.
- Although the direction may remain the same if the scalar is positive, the vector is still considered changed overall.
Conclusion
- Only option (a), the displacement parallel to itself, ensures that the vector is not changed.
- Understanding these transformations is essential in physics and engineering, particularly in vector analysis.
Vectors are mathematical entities characterized by both magnitude and direction. The options provided examine different transformations applied to a vector to determine if its essence remains unchanged.
Displacement Parallel to Itself
- When a vector is displaced parallel to its original direction, it retains its characteristics.
- The magnitude and direction remain constant, just shifted in space.
- This transformation does not alter the vector's identity, making it unchanged.
Rotation Through an Arbitrary Angle
- Rotating a vector alters its direction while maintaining the same magnitude.
- This transformation changes the vector's components, hence it is not unchanged.
Cross-Multiplication by a Unit Vector
- Cross-multiplying a vector by a unit vector results in a new vector that is perpendicular to both.
- This operation changes the vector's direction, hence it is not unchanged.
Multiplication by an Arbitrary Scalar
- Multiplying a vector by a scalar changes its magnitude.
- Although the direction may remain the same if the scalar is positive, the vector is still considered changed overall.
Conclusion
- Only option (a), the displacement parallel to itself, ensures that the vector is not changed.
- Understanding these transformations is essential in physics and engineering, particularly in vector analysis.
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