Final answer:
The question requires calculating the resultant displacement of consecutive vector movements in a plane. It involves breaking down movements into their north-south and east-west components and using vector addition to find the final position relative to the starting point.
Step-by-step explanation:
The question involves finding the resultant displacement from a starting point after performing consecutive vector displacements in different directions. This is a typical vector addition problem in physics or mathematics, where the displacement vectors need to be added head-to-tail to find the resultant displacement, magnitude, and direction. It also touches upon vector components and the commutative property of vector addition.
For instance, if Mike walks 455 miles due north, 700 miles due east, and then 710 miles due south, we can calculate his resultant displacement using vector addition by breaking down the movements into their north-south and east-west components. In this case, Mike ends up 255 miles south of his original latitude (because 710 - 455 = 255) and 700 miles east of his starting longitude. The resultant displacement can then be found using the Pythagorean theorem or vector addition formulas.