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Simple Vector Problem. Help please!

  1. Oct 11, 2005 #1
    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]- could be true, but im not sure why.
    If someone could guide me in the right direction i would be grateful. THANKS!
  2. jcsd
  3. Oct 11, 2005 #2

    Tom Mattson

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    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.) [itex]\vec{A}=3\hat{i}+4\hat{j}[/itex], [itex]\vec{B}=9\hat{i}+12\hat{j}[/itex]
    2.) [itex]\vec{A}=3\hat{i}+4\hat{j}[/itex], [itex]\vec{B}=5\hat{i}+13\hat{i}[/itex]
    3.) [itex]\vec{A}=3\hat{i}+4\hat{j}[/itex], [itex]\vec{B}=-3\hat{i}-4\hat{j}[/itex]
    4.) [itex]\vec{A}=3\hat{i}+4\hat{j}[/itex], [itex]\vec{B}=0\hat{i}+0\hat{j}[/itex]

    edited to add:

    Have you been taught the dot product of two vectors?
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