Two vectors have the magnitudes 5km and 10km. What are the maximum and minimum magnitudes of their vector sum?

Question

Two vectors have the magnitudes 5km and 10km. What are the maximum and minimum magnitudes of their vector sum?

Answer 1

Max 15 both same direction and add

Min 5 opposite directions

Answer 2

15 and 5

Answer 3

Suppose you walk 5km in a random direction. Then you turn randomly and walk another 10km. What's the furthest you could be from where you started? What's the closest? It should be obvious, the answers are 15km (both in same direction) and 5km (opposite directions).

Answer 4

As you know, a resultant is the final direction and magnitude as a result of two forces. So the maximum is if you go in the same direction. So maximum distance in this case is 15 km. Now the shortest distance. The shortest distance is the one in which you are closest to your starting point. So the vectors oppose each other. The resultant is 10-5= 5km.

Answer 5

Max is 15 km

Min is 5 km

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