When adding a vector of 6 units to a vector of 8 units, what is the possible magnitude of the resultant vector?

When adding a vector of 6 units to a vector of 8 units, what is the possible magnitude of the resultant vector?

• A. Exactly 2 units
• B. Exactly 10 units
• C. Exactly 14 units
• D. Between 2 and 14 units

Answer: (D)

When adding vectors, the resultant vector's magnitude depends on both the magnitudes of the vectors being added and the angle between them. The two vectors in this case have magnitudes of 6 units and 8 units. The minimum possible magnitude of the resultant occurs when the two vectors are oriented in exactly opposite directions. In this scenario, the resultant vector would have a magnitude equal to the difference between the two vectors: 8 units - 6 units = 2 units. Conversely, when the two vectors are oriented in the same direction, the resultant vector reaches its maximum magnitude, which is the sum of the two vectors: 6 units + 8 units = 14 units. Therefore, the possible magnitudes of the resultant vector can range anywhere between 2 units and 14 units, inclusive. This explains why the correct answer indicates that the magnitude of the resultant vector could be anywhere in that range, making the answer between 2 and 14 units.

When adding vectors, the resultant vector's magnitude depends on both the magnitudes of the vectors being added and the angle between them. The two vectors in this case have magnitudes of 6 units and 8 units.

The minimum possible magnitude of the resultant occurs when the two vectors are oriented in exactly opposite directions. In this scenario, the resultant vector would have a magnitude equal to the difference between the two vectors:

8 units - 6 units = 2 units.

Conversely, when the two vectors are oriented in the same direction, the resultant vector reaches its maximum magnitude, which is the sum of the two vectors:

6 units + 8 units = 14 units.

Therefore, the possible magnitudes of the resultant vector can range anywhere between 2 units and 14 units, inclusive. This explains why the correct answer indicates that the magnitude of the resultant vector could be anywhere in that range, making the answer between 2 and 14 units.