Question

What is the smallest magnitude possible for a resultant when adding a 6 unit vector to an 11 unit vector? What is the largest magnitude possible for a resultant when adding these vectors?

Option 1: Smallest = 0.545, Largest = 1.83
Option 2: Smallest = 9.2, Largest = 12.5
Option 3: Smallest = 36, Largest = 121
Option 4: Smallest = 5, Largest = 17

Answer 1

When adding a 6 unit vector to an 11 unit vector, the smallest magnitude of the resultant is 5 and the largest is 17, which occurs when the vectors are in opposite and the same directions, respectively.

Step-by-step explanation:

When adding two vectors, such as a 6 unit vector and an 11 unit vector, the smallest and largest magnitudes of the resultant depend on the angle between the two vectors. The smallest magnitude possible (the minimum magnitude) occurs when the vectors are in opposite directions, which would be the difference between their magnitudes, so 11 - 6 = 5. The largest magnitude possible (the maximum magnitude) occurs when the vectors are in the same direction, which would be the sum of their magnitudes, so 6 + 11 = 17.

Therefore, among the provided options, the correct answer would be Option 4: Smallest = 5, Largest = 17.