Final answer:
The third force F3 required to balance the given forces F1 and F2 is opposite in direction to the combined vector sum of F1 and F2. To achieve equilibrium, F3 = -((225.0/√2)(i-j)) N.
Step-by-step explanation:
To find the third force F3 that is needed to balance the first two forces, F1 and F2, we use the principle that the net force acting on the object must be zero when the forces are balanced. This is based on the concept of equilibrium in physics. Here, we have two forces F1 = 75.0/√2 (i-j) N and F2 = 150.0/√2 (i-j) N. Adding these vectors, we get a total force of F1 + F2 = (75.0/√2 + 150.0/√2)(i-j) N. This simplifies to (225.0/√2)(i-j) N.
To find F3, we need this third force to exactly counteract the combined effect of F1 and F2, meaning F3 must be equal in magnitude but opposite in direction to the sum of F1 + F2. So, F3 = -((225.0/√2)(i-j)) N, which ensures that the net force would be zero.