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Which of the following algebraic operations on vectors not permissible?
- a)adding any two vectors
- b)multiplying any vector by any scalar,
- c)multiplying the sum of vectors A and B by a scalar
- d)adding a scalar component of the vector to the same vector
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following algebraic operations on vectors not permissible...
Explanation:Although vectors and scalars represent different types of physical quantities, it is sometimes necessary for them to interact. While adding a scalar to a vector is impossible because of their different dimensions in space, it is possible to multiply a vector by a scalar.
Most Upvoted Answer
Which of the following algebraic operations on vectors not permissible...
Adding a scalar component of the vector to the same vector:
Vectors are mathematical objects that have both magnitude and direction. When we add a scalar component to a vector, we are changing the magnitude of the vector without changing its direction. This operation is not permissible in vector algebra because it violates the fundamental properties of vectors.
Explanation:
- Vectors can only be added or subtracted to other vectors, not to scalar components.
- Adding a scalar component to a vector would result in a quantity that is not a valid vector quantity.
- The addition of a scalar component does not preserve the direction of the original vector, which is a key property of vectors.
- In vector algebra, we can only add vectors to vectors or multiply vectors by scalars to scale their magnitude, but we cannot directly add scalar components to vectors.
Permissible operations on vectors:
- Adding any two vectors: We can add or subtract vectors to obtain a resultant vector.
- Multiplying any vector by any scalar: We can multiply a vector by a scalar to scale its magnitude.
- Multiplying the sum of vectors A and B by a scalar: We can multiply the sum of two vectors by a scalar to scale their combined magnitude.
In conclusion, the operation of adding a scalar component to the same vector is not permissible in vector algebra as it contradicts the fundamental properties of vectors. It is essential to understand the rules and properties of vectors to perform algebraic operations correctly.
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Which of the following algebraic operations on vectors not permissible?a)adding any two vectorsb)multiplying any vector by any scalar,c)multiplying the sum of vectors A and B by a scalard)adding a scalar component of the vector to the same vectorCorrect answer is option 'D'. Can you explain this answer?
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