I'm a bit confused about how to approach these questions. The only method that I have been using is trying to disprove options by counterexample to get to the solution.

Under what condition is: $\displaystyle |\vec A - \vec B| = A + B$

a) The magnitude of vectorBis zero.

|<-2, 7> - <0, 0>| = <-2, 7> + <0, 0 >

sqrt(53) = sqrt(53)

b) VectorsAandBare in the same direction.

|<2, 0> - <3, 0>| = <2, 0> + <3, 0>

1 != 13

c) VectorsAandBare in perpendicular directions.

|<2, 3> - <-1, 2>| = <2, 3> + <-1, 2>

sqrt(10) != ~4.84

d) VectorsAandBare in opposite directions.

|<3, 0> - <-3, 0>| = <3, 0> + <-3, 0>

6 = 6

e) The statement is never true

I'm very confused as to how to come to a definitive answer since a, d, and e are still in the game.

And I have to do $\displaystyle |\vec A - \vec B| = A - B$ next. :/