Question

Let the magnitudes of two displacement vectors be 4 m and 8 m, respectively. If the two vectors are added, the magnitude of the resultant vector. A. is exactly equal to 4 m. B. is exactly equal to 12 m. C. is greater than 12 m. D. could be as small as 4 m, and as large as 12 m

Answer 1

D. Could be as small as 4 m, and as large as 12 m.

Step-by-step explanation:

Since the magnitudes are vectors instead of scalars, their sum is not just the sum of their magnitudes; their directions must be taken in account. The maximum possible magnitude of the resultant occurs when both vectors have the same direction; in that case the resultant magnitude is the sum of the individual magnitudes (in this case, 12 meters). In the other hand, the minimum possible magnitude is when the vectors have opposite directions; in that case the magnitude of the resultant is the substraction of one magnitude to another (in this case, 4 meters). Finally, the right answer is D, because the possible values range from 4m to 12m.