Is it possible for a mineral to have a prismatic habit without having any cleavage? why or why not? if yes give an example.

Yes, this is possible for prismatic crystal habit to have no cleavage such as in the case of quartz. Quartz usually has well developed hexagonal prismatic crystals but at the same time has no cleavage. This indicates that the regular atomic structure with atoms aligned along preferential directions forming planes of cleavage does not occur in SiO2 which is the formula for quartz.