Final answer:
The statement that the magnitude of displacement will be the same if a person takes a wrong turn is False, because displacement considers direction. Distance traveled equals magnitude of displacement only in straight-line motion. The magnitude and direction of a resultant vector can be found if angles and magnitudes of the individual vectors are known.
Step-by-step explanation:
The question centers around the concept of the magnitude of displacement and its comparison to the actual distance traveled. For the given statement about a person who was supposed to walk 2 km east and then 1 km north but instead walks the second leg in the opposite direction, the statement is False. Displacement is a vector quantity, meaning it has both magnitude and direction. When the person takes a wrong turn, their displacement's direction changes, resulting in a different vector and thus a different magnitude of displacement than if they had followed the directions correctly.
Regarding circumstances where the distance traveled equals the magnitude of displacement, this occurs only when there is no change in direction; that is, the path taken between two points is a straight line. Whenever an object changes direction as it moves, the distance traveled will be greater than the magnitude of its displacement.
When dealing with vectors, it is indeed possible to find the magnitude and direction of the resultant vector if the magnitudes and angles of the individual vectors are known, by using vector addition methods such as the parallelogram law or trigonometric functions.