To determine the magnitude of force vector F2, the discussion revolves around calculating it using the resultant force and another known force. The resultant force is initially misstated as 199.9 N, but later clarified to be 58.264 N. Participants emphasize the need to break down the forces into their x and y components to solve for F2. There is confusion regarding the calculations and the diagram used, with requests for clarification on the components of F2. The conversation highlights the importance of showing work and understanding the algebra involved in solving for the unknown force.