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When a scalar quantity(if it has positive magnitude) is multiplies by a vector quantity the product is another vector quantity with the magnitude as the product of two vectors and the direction and dimensions same as the multiplied vector quantity
e.g. MOMENTUM
Multiplying or dividing vectors by scalars no more difficult than multiplying/dividing scalars by scalars. In order to do it, one simply divides the magnitude of the vector by the scalar, and doesn't change the direction of the vector. For example:
A vector: 60m/s [West]
Dividing that by 20 gives you 3m/s [West]
An example of division:
A vector: 34m [up]
Multiplying that by 5 gives you 170m [up]
An exception to this is when multiplying or dividing by a negative scalar, in which case the direction is reversed after the operation. For example:
A vector: 3N [45 degrees down from the horizontal, West]
Multiplying that by -10 gives you -30N [45 degrees down from the horizontal, West]
Or, in a more useful from: 30N [45 degrees up from the horizontal, East]
A scalar times a vector yields another vector.
The new vector has the same direction as the original vector and the new magnitude is equal to the product of the old magnitude and the scalar.
(Of course, if the scalar is a negative quantity, we understand that the new vector then points in the opposite direction as the original and the new magnitude is the absolute value of the product of the scalar and the old magnitude.)
In mathematics, the product of a scalar and vector is part of the definition of a vector space.
In physics, vectors satisfy the mathematical rules of a vector space.
When a scalar and a vector are multiplied together, it is called scalar multiplication. This operation involves multiplying each component of the vector by the scalar.
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What is the product of vector and scalar?
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
Is charge scalar or vector?
vector
What is speed a scalar or vector quantity?
scalar
Scalar and vector?
A scalar is a magnitude that doesn't specify a direction. A vector is a magnitude where the direction is important and is specified.
Is hours a vector or scalar quantity?
Hours is a scalar quantity, as it only represents the magnitude of time elapsed and does not have a direction associated with it.
How will you multiply a vector by positive number?
A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A negative scalar multiplied by the vector will reverse the direction by 180°.
Can vector quantity be divided and multiplied?
Vector quantities can be added and subtracted using vector addition, but they cannot be divided like scalar quantities. However, vectors can be multiplied in two ways: by scalar multiplication, where a scalar quantity is multiplied by the vector to change its magnitude, or by vector multiplication, which includes dot product and cross product operations that result in a scalar or vector output.
When a vector is multiplied by a scalar physical quantitythen what will be dimensions of resulting vector?
The same as the original vector. The scalar will change the numbers, but not the dimensions.
Multiplying or dividing vectors by scalars results in what?
When multiplying a vector by a scalar, each component of the vector is multiplied by the scalar. This operation changes the magnitude of the vector but not its direction. Similarly, dividing a vector by a scalar involves dividing each component of the vector by the scalar.
Can a scalar quantity be the product of 2 vector quantities?
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
When does a vector remain unchanged?
A vector remains unchanged when it is multiplied by a scalar of 1. This is because multiplying a vector by a scalar of 1 effectively scales the vector without changing its direction.
Is the cross product vector or scalar?
The cross product is a vector. It results in a new vector that is perpendicular to the two original vectors being multiplied.
What is a scalar times a vector?
A scalar times a vector is a vector.
Is inertia is a scalar or vector?
vector
How do you add scalar?
To add a scalar to a vector, you simply multiply each component of the vector by the scalar and then add the results together to get a new vector. For example, if you have a vector v = [1, 2, 3] and you want to add a scalar 5 to it, you would calculate 5*v = [5, 10, 15].
What is the product of vector and scalar?
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
What are the quantities that identifies scalar and vector quantities?
A vector is characterized by having not only a magnitude, but a direction. If a direction is not relevant, the quantity is called a scalar.
