If you have given examples in which |A+ B|= |A|+ |B| the anyone of those is a counter-example to (e).
But for (a), (b), (c), and (d) if you are trying to prove that under each of those conditions, |A+ B|= |A|+ |B|, an example is NOT a proof.
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:
a) The magnitude of vector B is zero.
|<-2, 7> - <0, 0>| = <-2, 7> + <0, 0 >
sqrt(53) = sqrt(53)
b) Vectors A and B are in the same direction.
|<2, 0> - <3, 0>| = <2, 0> + <3, 0>
1 != 13
c) Vectors A and B are in perpendicular directions.
|<2, 3> - <-1, 2>| = <2, 3> + <-1, 2>
sqrt(10) != ~4.84
d) Vectors A and B are 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 next. :/
If you have given examples in which |A+ B|= |A|+ |B| the anyone of those is a counter-example to (e).
But for (a), (b), (c), and (d) if you are trying to prove that under each of those conditions, |A+ B|= |A|+ |B|, an example is NOT a proof.
I think that they want me to find the magnitudes of vectors A and B on the right side, then sum them to see if the scalar values are equivalent on each side. The problem is that I don't know how to do that without using specific chosen values.
I agree that the right side of the equation is confusing, but that was how it was written in the book.