Final answer:
The largest magnitude of the resultant displacement vector →R is 26 m when the vectors A and B are in the same direction, and the smallest magnitude is 14 m when they are in opposite directions.
Step-by-step explanation:
The magnitudes of two displacement vectors A and B are given to be A = 20 m and B = 6 m, and you are asked to find the largest and smallest values of the magnitude of their resultant →R = →A + →B.
The largest value of →R occurs when the vectors A and B are pointed in the same direction, in which case their magnitudes simply add up, so the largest magnitude is 20 m + 6 m = 26 m.
The smallest value of →R happens when the vectors are pointed in exactly opposite directions, and thus their magnitudes subtract; the smallest magnitude is 20 m - 6 m = 14 m. Therefore, the answer is a) Largest: 26 m; Smallest: 14 m.