Two vectors with magnitudes of 6 meters and 8 meters cannot have a resultant of:
48 meters
14 meters
10 meters
2 meters
If they were pointing in the same direction, it would be 14, if in the opposite direction, 2 meters. So anything between 2 and 14 is valid.
To determine whether two vectors with magnitudes of 6 meters and 8 meters can have a resultant of a certain magnitude, we can use the Triangle Inequality theorem. According to this theorem, the sum of the magnitudes of any two sides of a triangle must be greater than or equal to the magnitude of the third side.
In this case, we have two vectors with magnitudes of 6 meters and 8 meters. Let's consider the possible magnitudes for the resultant:
1. 48 meters:
To find out if a resultant of 48 meters is possible, we add the magnitudes of the two vectors: 6 + 8 = 14 meters. Since 14 meters is less than 48 meters, it is not possible for the resultant to be 48 meters.
2. 14 meters:
Again, we add the magnitudes of the two vectors: 6 + 8 = 14 meters. Since the sum of the magnitudes matches the given resultant magnitude of 14 meters, it is possible for the two vectors to have a resultant of 14 meters.
3. 10 meters:
We add the magnitudes of the two vectors: 6 + 8 = 14 meters. Similar to the first case, the sum of the magnitudes is greater than 10 meters, so it is possible for the two vectors to have a resultant of 10 meters.
4. 2 meters:
Once more, we add the magnitudes of the two vectors: 6 + 8 = 14 meters. As in the previous cases, the sum of the magnitudes exceeds 2 meters, so it is possible for the two vectors to have a resultant of 2 meters.
Therefore, based on the Triangle Inequality theorem, the only magnitude that two vectors with magnitudes of 6 meters and 8 meters cannot have as a resultant is 48 meters.