Question

What is scalar quantity??​

Answer 1

Answer:

A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector.

Explanation:

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Answer 2

Explanation:

In mathematics scalars are elements of an algebraic structure field when we are talking about another algebraic structure vector space over the field in which the field is used to define this structure. In physics scalars (or scalar quantities) are quantities that are unaffected by changes to a vector space basis (i.e., a coordinate system transformation) and are often accompanied by units of measurement, as in "10 cm". A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change. This physical definition of scalars, in classical theories, like Newtonian mechanics, means that rotations or reflections preserve scalars, while in relativistic theories, Lorentz transformations or space-time translations preserve scalars.

A quantity that is a physically scalar (as being not changed by a change of a vector space basis) is also mathematically a scalar (as an element of a field used to define a vector space). The magnitude (or length) of an electric field vector is calculated as the square root of the inner product of the electric field with itself and the outcome of the inner product is an element of the field for the vector space in which the electric field is described. As the field for the vector space in this example and usual cases in physics is the field of real numbers or complex numbers, the square root of the inner product is also an element of the field so it is a mathematically scalar. Since the inner product is independent of any vector space basis, the electric field magnitude is also a physically scalar. For a mass of an object that is unaffected by a change of a vector space basis so is a physically scalar, it is described by a real number as an element of the real number field. Since a field F is a vector space F over a field F, where addition defined on F is vector addition and multiplication defined on F is scalar multiplication, the mass is also a mathematically scalar. Other quantities such as a distance, charge, volume, time, speed (the magnitude of a velocity vector)[1] are also mathematically and physically scalars in similar senses.