Simple Vector Problem. Help please!

[antiflag403]

Hey everyone,
I realize that this is a pretty simple problem but i cant 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 im pretty sure thats wrong.
For B I dont think both C=A+B and [C]=[A]-[B] could be true, but im not sure why.
If someone could guide me in the right direction i would be grateful. THANKS!

[Tom Mattson]

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?