Q:

Vector SAT MATH 2

If the magnitudes of vectors a and b are 5 and 12, respectively, then the magnitude of vector (b-a) could NOT be:
a) 5
b) 7
c) 10
d) 12
e) 17
The answer is 5. But I am not sure which theorem I should use to go about this problem. Triangle inequality theorem? Help is appreciated!

A:

By triangle inequality:
$$|b|-|a|\le |a-b| \le |a|+|b|\to 7\le |a-b| \le 17$$

