To solve this problem, we need to use vector addition. The goal is to find a third force, F3, that when added to the given forces, F1 and F2, results in a zero resultant force (or net force).
Step 1: Represent the forces as vectors
Draw a diagram and represent each force as a vector. In this case, F1 is directed due east, and F2 is directed due north. To represent these vectors, draw arrows with lengths proportional to the magnitudes of the forces, and label their directions.
Step 2: Add the two given forces
To get the resultant force, we need to add F1 and F2 together. To do this, place the tail of F2 (the force pointing north) at the head of F1 (the force pointing east). The vector from the tail of F1 to the head of F2 represents the sum or resultant force, and it should point from the initial position of F1 to the final position of F2.
Step 3: Find the magnitude and direction of the third force, F3
Since the resultant force is zero, we need to find the vector that cancels out the sum of F1 and F2. In other words, we need to find a vector that points in the opposite direction and has the same magnitude as the resultant force.
To do this, reverse the direction of the resultant vector (head to tail), and you will find F3. The magnitude of F3 will be the same as the resultant force, and its direction will be the opposite of the resultant force.
Step 4: Calculate the magnitude and direction of F3
In this case, since both F1 and F2 have magnitudes of 2.0 N, the magnitude of the resultant force will also be 2.0 N.
Now, reversing the direction of the resultant force, we find that F3 should have a magnitude of 2.0 N and should be directed towards the southwest (opposite direction to the resultant force).
Thus, the magnitude of the third force, F3, is 2.0 N, and its direction is southwest.