Final answer:
The statement regarding critical paths is true, as multiple longest-duration paths in a network are considered critical. Displacement remains the same regardless of the path order, making the statement about different displacements false. The use of the Pythagorean theorem to calculate the resultant vector length of perpendicular vectors is true.
Step-by-step explanation:
The statement 'If two paths are tied up for the longest duration, both would be considered to be critical paths' is true. In project management and network planning, a critical path is the sequence of stages determining the minimum time needed for an operation. If two or more paths through the network have the longest duration, they are all considered critical paths because they both have the potential to delay the entire project if any of their stages are delayed.
The statement 'The displacement of the first person will be more than the displacement of the second person' is false. Displacement in physics refers to the change in an object's position as a straight line from the start point to the end point. If two people walk the same vector path, regardless of the order of the steps, their displacement will be the same.
The statement 'We can use the 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. In physics, when two vectors are at a right angle, the Pythagorean theorem is a useful tool for finding the magnitude of the resultant vector.