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Which of the following statements.is false regarding the vectors?
- a)The magnitude of a vector is always a scalar
- b)Each component of a vector is always a scalar
- c)Two vectors having different magnitudes cannot have their resultant zero
- d)Vectors obey triangle law of addition
Correct answer is option 'B'. Can you explain this answer?
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Which of the following statements.is false regarding the vectors?a)The...
The magnitude of a vector is a pure number. Each component of a vector is also a vector. The resultant of two vectors can be zero only if they have the same magnitude and opposite directions.
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Which of the following statements.is false regarding the vectors?a)The...
False Statement: The false statement regarding the vectors is option B: Each component of a vector is always a scalar.
Explanation:
1. Magnitude of a Vector:
The magnitude of a vector represents its size or length. It is always a scalar quantity. Magnitude is a positive value and does not have any direction associated with it. It gives information about the magnitude or intensity of a physical quantity.
2. Components of a Vector:
A vector can be resolved into two or three components based on the coordinate axes. These components are scalar quantities that represent the projection of the vector along each coordinate axis. The components can be positive, negative, or zero, depending on the direction and orientation of the vector.
3. Resultant of Vectors:
The resultant vector is obtained by adding two or more vectors using the triangle law of addition. The triangle law states that if two vectors are represented by two sides of a triangle, then the third side represents the resultant vector. The resultant vector can have different magnitudes and directions, depending on the magnitudes and directions of the original vectors.
False Statement:
Option B: Each component of a vector is always a scalar.
This statement is false because the components of a vector can be either scalar or vector quantities, depending on the system of representation. In Cartesian coordinate systems, the components of a vector are scalar quantities. However, in polar or spherical coordinate systems, the components of a vector are vector quantities.
Conclusion:
Vectors have both magnitude and direction. The magnitude of a vector is always a scalar, and the components of a vector can be either scalar or vector quantities, depending on the system of representation. The statement in option B is false.
Explanation:
1. Magnitude of a Vector:
The magnitude of a vector represents its size or length. It is always a scalar quantity. Magnitude is a positive value and does not have any direction associated with it. It gives information about the magnitude or intensity of a physical quantity.
2. Components of a Vector:
A vector can be resolved into two or three components based on the coordinate axes. These components are scalar quantities that represent the projection of the vector along each coordinate axis. The components can be positive, negative, or zero, depending on the direction and orientation of the vector.
3. Resultant of Vectors:
The resultant vector is obtained by adding two or more vectors using the triangle law of addition. The triangle law states that if two vectors are represented by two sides of a triangle, then the third side represents the resultant vector. The resultant vector can have different magnitudes and directions, depending on the magnitudes and directions of the original vectors.
False Statement:
Option B: Each component of a vector is always a scalar.
This statement is false because the components of a vector can be either scalar or vector quantities, depending on the system of representation. In Cartesian coordinate systems, the components of a vector are scalar quantities. However, in polar or spherical coordinate systems, the components of a vector are vector quantities.
Conclusion:
Vectors have both magnitude and direction. The magnitude of a vector is always a scalar, and the components of a vector can be either scalar or vector quantities, depending on the system of representation. The statement in option B is false.
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Which of the following statements.is false regarding the vectors?a)The magnitude of a vector is always a scalarb)Each component of a vector is always a scalarc)Two vectors having different magnitudes cannot have their resultant zerod)Vectors obey triangle law of additionCorrect answer is option 'B'. Can you explain this answer?
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