You are adding vectors of length 20 and 40 units. Which of the following choices is a possible resultant magnitude?

a. 64

b. 18

c. 0

d. 100

e. 37

Answer: e. 37

Explanation:

When two vectors are added, the maximum and minimum posible values, happen when both vectors are aligned each other.

If both vectors aim in the same direction, the maximum value is just the arithmetic sum of their lengths, in this case, 60.

If they aim in opposite direction, the resultant is the substraction of their magnitudes, which yields 20.

Any other posible value (depending on the angle between vectors, which can span from 0º to 180º) must be between those values.

So, the only choice that fits within this interval, is 37.