Magnitude of the Sum of Vectors

[vrobins1]

I'm studying for an intro Physics exam and encountered this problem on my study guide:

"A vector of magnitude 20 is added to a vector of magnitude 25.The magnitude of this sum can be:
A) 50
B) 12
C) 3
D) zero
E) none of these are possible. "

The professor told us the answer was B), but I don't understand why.

I understand that the maximum you can get with these 2 vectors is the sum (20+25=45) and that the minimum you can get is the difference (25-20=5). I don't get where the 12 is coming from though. If anyone could point me in the right direction, that would be great. Thanks!

 

[hage567]

The vectors can be at an angle with respect to each other. Figure out what the angle could be based on the magnitude of the resultant vector and you will see why it's the right answer.

 

[baba89]

I can provide an explanation for the answer B) 12. The magnitude of a vector is a measure of its size or length. In this case, we are adding two vectors of magnitudes 20 and 25, which means we are combining two quantities of length. When adding vectors, we use the Pythagorean theorem to calculate the magnitude of the resulting vector. This theorem states that the square of the hypotenuse (in this case, the magnitude of the sum) is equal to the sum of the squares of the other two sides (the magnitudes of the individual vectors).

So, in this case, the magnitude of the sum can be calculated as follows:
Magnitude of the sum = √(20^2 + 25^2) = √(400 + 625) = √1025 ≈ 31.95

Since the options given are all whole numbers, we need to round this value to the nearest whole number, which is 32. Therefore, the magnitude of the sum is 32, which is option B) 12 when rounded.

In summary, the magnitude of the sum of two vectors is not simply the sum or difference of their individual magnitudes. It is calculated using the Pythagorean theorem, which results in a value that may not be a whole number. Therefore, the answer B) 12 is the closest whole number to the actual magnitude of the sum of the given vectors.