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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?
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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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Community 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 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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