Final answer:
The statement is false because displacement is a vector quantity that includes both magnitude and direction. Incorrectly following directions changes the displacement from the original intended path.
Step-by-step explanation:
The statement 'displacement will be the same as it would have been had he followed directions correctly' can be considered false. Displacement is a vector quantity, meaning it not only considers magnitude, but also the direction of the movement. If directions are not followed correctly, the path taken could lead to a different endpoint, which means the displacement - the straight line between start and end point - may be different.
For example, if you are supposed to travel straight east for 5 km, but you travel 3 km east and then 4 km north, your displacement is not the same as the 5 km east you were instructed to follow. Instead, your actual displacement would be calculated using the Pythagorean theorem, giving a result different from the original displacement of 5 km east.