State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(i) Adding any two scalars (ii) Adding a scalar to a vector of the same dimensions
(iii) Multiplying any vector by any scalar (iv) Multiplying any two scalars
(v) Adding any two vectors

Solution: a) No, because only the scalars of same dimensions can be added.
b) No, because a scalar cannot be added to a vector.
c) Yes, multiplying a vector with a scalar gives thje scalar (number) times the vector quantity which makes sense and one gets a bigger vector. for example, when acceleration A is multiplied mass m, we get a force F=ml
d) Yes, two scalas multiplied yield a meaningful result, for example multiplication of rise in temperature of water and its mass gives the amount of heat absorbed by that mass of water.
e) No, because the two vectors of same directioins can be added.
f) Yes, because both are vectors of the same dimensions.