The insight: a force vector naturally groups three related values. Create a struct with x, y, and z fields. This keeps coordinates together instead of scattered across separate variables.
You don't need to store all vectors. Keep a running sum instead. Start with a sum struct initialized to (0, 0, 0). As you read each force, add its components to your sum's x, y, and z fields.
After processing all forces, check if the sum equals (0, 0, 0). Equilibrium means every component cancels out. One non-zero component breaks equilibrium.