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
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.
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A scalar is a magnitude that doesn't specify a direction. A vector is a magnitude where the direction is important and is specified.
Hours is a scalar quantity, as it only represents the magnitude of time elapsed and does not have a direction associated with it.
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°.
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.
The same as the original vector. The scalar will change the numbers, but not the dimensions.
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.
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.
The significance of the divergence of a scalar times a vector in vector calculus is that it simplifies to the scalar multiplied by the divergence of the vector. This property is important in understanding how scalar fields interact with vector fields and helps in analyzing the flow and behavior of physical quantities in various fields of science and engineering.
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.
The cross product is a vector. It results in a new vector that is perpendicular to the two original vectors being multiplied.
A scalar times a vector is a vector.
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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].
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.