Vectors
,
,and
Have magnitudes 6,11,and 22.When these vectors are added,what is the least possible magnitude of their addition?

Question

Vectors 
, 
,and 
Have magnitudes 6,11,and 22.When these vectors are added,what is the least possible magnitude of their addition?

Quizplus · Accepted Answer

The triangle inequality states that the magnitude of the sum of two vectors is always greater than or equal to the difference of their magnitudes. Therefore, in order to minimize the magnitude of the sum of the three given vectors, we should try to make the sum of any two vectors as close to the magnitude of the third vector as possible.

If we add vectors (a) and (b), we get a magnitude of 17, which is closer to the magnitude of vector (c) than the magnitudes of (a) and (b) individually. Therefore, the minimum magnitude of the sum of the three vectors is 22 - 17 = 5, which is choice C.

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