State with reasons whether the following algebric operations with scalar and vector phisical 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) multiplaying any two scalars
(e) adding any two vectors
(f) adding a component of a vector to the same vector .

Explanation

(a) It is not meaningful as we can add only those scalars which have same dimension .
(b) It is not meaningful because a scalar has no direction whereas a vector has a direction.
(c) It is meaningful . For example , if we multiply mass with acceleration , we get a new phisical quantity Force, which is a vector quantity.
(d) Multiplying any two scalars is a meaningful operation.
(e) It is not meaningful because only the vectors having same nature can be added.
(f) It is meaningful . Because the component of a vector and the original vector have same dimensions.