37. 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

a) 5

Step-by-step explanation:

Graphically, b - a can be represented by placing a vector of the same magnitude of a but opposite orientation at the end of vector b. Let's call this vector - a. |b-a| will be the vector that share origin with b and end with - a. The minimum value that the magnitude of |b-a| can have will occur when - a have the same direction of b but opposite orientation, and the maximum value when - a have the same direction and orientation. Mathematically, this would be:

|b-a|min = 12 - 5 = 7

|b-a|max = 12 - (-5) = 17

Notice that 5 is the only option that is not in this range, so the answer is a.