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Which one of the following operations is valid?
- a)Vector multiplied by scalar
- b)Vector added to scalar
- c)Vector subtracted from scalar
- d)Vector divided by vector
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following operations is valid?a)Vector multiplied by ...
Only operations valid for vector with scalars are multiplication and division. A vector can be multiplied or divided by a scalar. Other operations like addition and subtraction are not valid for vectors with scalars.
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Which one of the following operations is valid?a)Vector multiplied by ...
Vector multiplied by scalar
- In mathematics, a vector is a quantity that has both magnitude and direction. It can be represented by an arrow, where the length represents the magnitude and the direction represents the direction.
- A scalar, on the other hand, is a quantity that has only magnitude and no direction. Examples of scalars include temperature, mass, and time.
- When a vector is multiplied by a scalar, each component of the vector is multiplied by the scalar. The result is a new vector that has the same direction as the original vector but with a magnitude that is scaled by the scalar.
- This operation is valid because it follows the rules of vector multiplication and scalar multiplication.
Example:
Let's consider a vector V = (2, -3) and a scalar k = 4.
V * k = (2 * 4, -3 * 4) = (8, -12)
The resulting vector (8, -12) has the same direction as the original vector (2, -3) but with a magnitude that is 4 times larger.
- In terms of physics, multiplying a vector by a scalar can represent scaling the magnitude of a physical quantity while keeping the direction unchanged. For example, if a vector represents a displacement, multiplying it by a scalar can represent stretching or compressing the displacement without changing the direction.
- Vector multiplication by a scalar is a fundamental operation in linear algebra and has various applications in physics, engineering, and computer science. It allows us to manipulate and analyze vectors in a more efficient and meaningful way.
- In mathematics, a vector is a quantity that has both magnitude and direction. It can be represented by an arrow, where the length represents the magnitude and the direction represents the direction.
- A scalar, on the other hand, is a quantity that has only magnitude and no direction. Examples of scalars include temperature, mass, and time.
- When a vector is multiplied by a scalar, each component of the vector is multiplied by the scalar. The result is a new vector that has the same direction as the original vector but with a magnitude that is scaled by the scalar.
- This operation is valid because it follows the rules of vector multiplication and scalar multiplication.
Example:
Let's consider a vector V = (2, -3) and a scalar k = 4.
V * k = (2 * 4, -3 * 4) = (8, -12)
The resulting vector (8, -12) has the same direction as the original vector (2, -3) but with a magnitude that is 4 times larger.
- In terms of physics, multiplying a vector by a scalar can represent scaling the magnitude of a physical quantity while keeping the direction unchanged. For example, if a vector represents a displacement, multiplying it by a scalar can represent stretching or compressing the displacement without changing the direction.
- Vector multiplication by a scalar is a fundamental operation in linear algebra and has various applications in physics, engineering, and computer science. It allows us to manipulate and analyze vectors in a more efficient and meaningful way.
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Which one of the following operations is valid?a)Vector multiplied by scalarb)Vector added to scalarc)Vector subtracted from scalard)Vector divided by vectorCorrect answer is option 'A'. Can you explain this answer?
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