question_answer 4)

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) No. Only two such scalars can be added which represent the same physical quantity. (b) No. A scalar cannot be added to a vector even of same dimensions because a vector has a direction while a scalar has no direction e.g., speed cannot be added to velocity. (c) Yes. We can multiply any vector by a scalar. For example, when mass (scalar) is multiplied with acceleration (vector), we get force (vector) i.e., . (d) Yes. We can multiply any two scalars. When we multiply power (scalar) with time (scalar), we get work done (scalar) i.e., W = Pt. (e) No. Only two vectors of same nature can be added by using the law of vector addition. (f) No. A component of a vector can be added to the same vector only by using the law of vector addition. So the addition of a component of a vector to the same vector is not a meaningful algebraic operation.