When Does Vector Addition Equal the Sum of Magnitudes?

[antiflag403]

Hey everyone,
I realize that this is a pretty simple problem but i can't seem to wrap my brain around it. If someone could point me in the right direction i would be thankful.
suppose (vector)C= (vector)A + (vector)B
a) under what circumstances does [(vector)C]= [(vector)A] + [(vector)B]? ( [ ]= absolute value)
b) could [(vector)C]= [(vector)A] - [(Vector)B]? if so how? if not, why not?
ok. for A i was thinking the only way that could be true is if both A and B had the same sign, but I am pretty sure that's wrong.
For B I don't think both C=A+B and [C]=[A]- could be true, but I am not sure why.
If someone could guide me in the right direction i would be grateful. THANKS!

 

[quantumdude]

I think that you'll go a long way in understanding this if you try out some examples.

Why don't you try to check your equalities with the following:

1.) $\vec{A}=3\hat{i}+4\hat{j}$, $\vec{B}=9\hat{i}+12\hat{j}$
2.) $\vec{A}=3\hat{i}+4\hat{j}$, $\vec{B}=5\hat{i}+13\hat{i}$
3.) $\vec{A}=3\hat{i}+4\hat{j}$, $\vec{B}=-3\hat{i}-4\hat{j}$
4.) $\vec{A}=3\hat{i}+4\hat{j}$, $\vec{B}=0\hat{i}+0\hat{j}$

edited to add:

Have you been taught the dot product of two vectors?