How Do Vector Magnitudes Relate in Simple Equations?

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Vector magnitudes relate in equations through specific conditions. For the equation C = A + B, the absolute values can equal each other only if vectors A and B point in the same direction, leading to |C| = |A| + |B|. However, the equation |C| = |A| - |B| is not valid in vector terms, as it contradicts the principles of vector addition, where direction plays a crucial role. The discussion emphasizes the importance of considering vector direction when analyzing their magnitudes. Understanding these relationships is essential for solving vector problems accurately.
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Hey everyone,
I know this problem is easy but I am having some trouble. If someone could point me in the right direction i would be really grateful.
Suppose (vector)C=(vector)A + (vector)B
a) under what circumstances does [A]=+[C]?
b) Could [C]=[A]-?
( [ ]= absolute value)
Ok. For A i think that A and B would have to have the same signs but I am really not to sure.
For B i can't see how C=A+B can be equal to [C]=[A]-. It seems like a simple contradiction, which usually means I am wrong. :-p
I would really apprecitate some help!
 
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Try drawing any two random vectors A and B on a piece of paper. Then draw vector C = A + B. Is it possible for you to draw A and B such that the lengh of A plus the length of B is equal to the length of C?
 
Antiflag - for (a), did you mean |C| = |A| + |B|? That's the question Tzar hinted at.

For (b), you were on the right track with your other answer. Think: the difference between vector addition and scalar addition is that vectors have direction. Does the - sign have any meaning with respect to direction?
 

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