Question

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful: (a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.

Answer 1

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

(a) adding any two scalars,

(b) adding a scalar to a vector of the same dimensions,

(c) multiplying any vector by any scalar,

(d) multiplying any two scalars,

(e) adding any two vectors,

(f) adding a component of a vector to the same vector.

Answer

(a) Meaningful

(b) Not Meaningful

(c) Meaningful

(d) Meaningful

(e) Meaningful

(f) Meaningful

Explanation:

(a)The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.

(b)The addition of a vector quantity with a scalar quantity is not meaningful.

(c) A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.