Which joint directorates staff organization is responsible for operations?

The J3 directorate is responsible for operations within a joint staff organization. This includes the planning and execution of military operations, training, and the management of joint operational forces. The J3 is tasked with coordinating and overseeing the actual military operations, ensuring that the strategic goals set by higher command are effectively implemented on the ground.

In contrast, other directorates focus on different aspects of joint staff responsibilities. For instance, J2 is dedicated to intelligence operations, gathering and analyzing information to support decision-making. J4 handles logistics, ensuring that resources, supplies, and personnel are efficiently managed and sustained throughout operations. J5 focuses on strategic planning, which involves the long-term formulation of operational strategies and policies. Thus, the specific role of J3 in managing operations makes it the correct answer for this question.