Final answer:
The statement that the magnitude of the total displacement remains the same even if a person walks in the opposite direction for the second leg of their trip is false because the final displacement will be in a southeast direction rather than northeast.
Step-by-step explanation:
The statement that a person is following a set of directions to walk 2 km east and then 1 km north, but instead takes a wrong turn and walks in the opposite direction for the second leg of the trip, and the magnitude of his total displacement will be the same as it would have been had he followed directions correctly is false. If the person walks 1 km in the opposite direction, instead of north, they would end up walking 1 km south, making the path and resulting displacement different.
In fully understanding the situation: If the person walks 2 km east and 1 km north the resulting displacement will be in a northeast direction from the starting point. However, if the person walks 2 km east and then 1 km south (the opposite direction of north), the resulting displacement will be in a southeast direction from the starting point. These two different paths will have different displacements; therefore, the initial statement is incorrect.