Vector Addition: Calculate Magnitude of Sum

[joej24]

Homework Statement

A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
a. zero
b. 3
c. 12
d. 47
e. 50

Homework Equations

c ^2 = a^2 + b^2

The Attempt at a Solution

I was not entirely sure on what to do. I tried using the Pythagorean theorem to find the resultant of the 2 vectors and got 32. ( c ^2 = 20^2 + 25^2).
The answer by the way is C.

Thanks!
Joe

 

[betel]

Try do add the vectors in different ways. Then you will get a possible maximal and a minimal value for the magnitude of the resulting vector. All but one possible answers are outside of this region.

 

[joej24]

okay. I got it. The max magnitude of their addition would be when they are parallel in the same direction. mag would = 45. The min would be when they are parallel in the opposite direction. mag would = 5. Therefore the answer is 12. Thanks!

 

[betel]

Good.