Answer the questions that follow about the relationship between two non-zero vectors.
a. (i) Explain the mathematical meaning of the terms "parallel" and "anti-parallel" when applied to vectors.
b. (ii) Show how the sign of a⋅b, in comparison with ∣a∣∣b∣, distinguishes between vectors that are parallel, anti-parallel or neither.
c. (iii) Provide one example each of a pair of vectors that are (a) parallel, (b) anti-parallel, and (c) perpendicular, stating the value of the dot product in each case.