Final answer:
The use of the Pythagorean theorem to find the length of a resultant vector from two perpendicular vectors is correct. Displacement is the same regardless of the order in which the same distances are covered in any direction, making the statement about different displacements false.
Step-by-step explanation:
The statement "We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other" is true. When two vectors are perpendicular (at right angles), they can form the two legs of a right-angle triangle. The resultant vector is the hypotenuse of that triangle, and we can use the Pythagorean theorem to find its length.
For instance, if a person walks 2 blocks east and 5 blocks north, they have formed a right-angle path representing two perpendicular vectors. By applying the Pythagorean theorem (a2 + b2 = c2), where a is 2 blocks and b is 5 blocks, we can determine the displacement (c) as the square root of (22 + 52) which equals the square root of 29 blocks.
Regarding displacements, the question about two people walking in different orders but covering the same distances east and north implies that displacement is independent of the path taken. Therefore, their displacements will be the same, making the statement false.