Answer the following questions related to unit vectors.
a. (i) Define a unit vector. Distinguish between a scalar and a vector with one suitable example of each.
b. (ii) Show mathematically that dividing any non-zero vector by its own magnitude yields a vector of magnitude unity.
c. (iii) Describe, with one explicit example from daily life, why expressing a physical quantity in terms of its unit vector components is advantageous when solving three-dimensional problems.