$(a)$ Why is hard water not suitable for washing clothes with soap?
$(b)$ Why does micelle formation take place when soap is added to water?
$(c)$ What is saponification?

(N/A) Hard water contains dissolved salts of calcium and magnesium. When soap is added to hard water,it reacts with these ions to form an insoluble precipitate known as scum. This prevents the formation of lather,making it ineffective for cleaning.
$(b)$ Soap molecules have a dual nature: a hydrophilic (water-loving) head and a hydrophobic (water-repelling) hydrocarbon tail. When added to water,the hydrophobic tails cluster together to avoid water,while the hydrophilic heads face outward toward the water,resulting in the formation of spherical structures called micelles.
$(c)$ Saponification is the chemical process in which an ester is reacted with an alkali (like sodium hydroxide) to produce soap (a salt of a fatty acid) and alcohol (glycerol).