State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful : (a) Addition of any two scalars (b) Adding a scalar to a vector which has the same dimensions (c) Multiplying a vector by any scalar (d) Multiplying any two scalars (e) Adding any two vectors (f) Addition of a vector component to the same vector.
(a) Yes, addition of two scalar quantities is meaningful only if they both represent the same physical quantity. (b) No, addition of a vector quantity with a scalar quantity is not meaningful. (c) Yes, scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse. (d) Yes, scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions. (e) Yes, addition of two vector quantities is meaningful only if they both represent the same physical quantity. (f) Yes, component of a vector can be added to the same vector as they both have the same dimensions.
