Question

Two vectors with magnitudes of 4 meters and 3 meters cannot have a resultant of

3 meters
4 meters
7 meters
8 meters

Answer 1

8 meters

Step-by-step explanation:

The maximum magnitude of the resultant of two vectors is obtained when the two vectors are parallel to each other. In this case, in fact, their resultant will be on the same line, and so the magnitude of the resultant will be equal simply to the sum of the magnitude of the two vectors.

In this case, therefore, the maximum magnitude of the resultant is:

`|R| = A + B = 4 + 3 = 7 m`

On the contrary, the minimum magnitude of the resultant of two vectors is obtained when the two vectors are anti-parallel, which means that the two vectors are exactly in opposite directions. In this case, the resultant is simply obtained by calculating the difference between the magnitude of the two vectors, and its direction will be in the direction of the longest vector among the two. In this case, therefore, it will be

`|R| = A - B = 4-3 = 1 m`

in the direction of the longer vector (4 m).

These results correspond to the most extreme cases, where the angle between the two vectors is
`0^(\circ)` (first case) or
`180^(\circ)` (second case). In all the intermediate cases, the magnitude of the resultant vector will be in the interval between the maximum and minimum value, therefore in the interval

[1 m, 7 m]

Therefore, among the option given, 8 meters is not a possible result.