Question

Suppose you add two vectors A and B. What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?

a) The greatest magnitude is when the vectors are perpendicular; the smallest is when they are collinear.

b) The greatest magnitude is when the vectors are collinear; the smallest is when they are perpendicular.

c) The greatest magnitude is when the vectors are antiparallel; the smallest is when they are parallel.

d) The greatest and smallest magnitudes are the same for any relative direction between the vectors.

Answer 1

The relative direction between two vectors that produces the greatest magnitude of the resultant vector is when the vectors are collinear. The maximum magnitude of the resultant vector is obtained by summing the magnitudes of vectors A and B. On the other hand, the relative direction that produces the smallest magnitude is when the vectors are perpendicular to each other.

Step-by-step explanation:

In order to find the relative direction that produces the resultant with the greatest magnitude, we need to consider the properties of vector addition. The greatest magnitude is achieved when the vectors are collinear, meaning they are parallel and have the same direction. This is option b). The maximum magnitude of the resultant vector is obtained by summing the magnitudes of vectors A and B.

On the other hand, to find the relative direction that produces the smallest magnitude, we need to consider the properties of vector subtraction. The smallest magnitude is achieved when the vectors are perpendicular to each other. This is option a). The minimum magnitude of the resultant vector is zero if vectors A and B have the same magnitude and are pointing in opposite directions.