Angle Between a & b When |a| = |b| = |a-b| or |a+b|

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When vectors a and b satisfy |a| = |b| = |a-b|, the angle between them is 120 degrees, indicating they are not equal but symmetrically positioned. Conversely, if |a| = |b| = |a+b|, the angle between a and b is 0 degrees, meaning they are identical vectors. The initial assumption that |a| = |b| implies a = b is incorrect, as different vectors can have the same magnitude. The discussion highlights the importance of understanding vector relationships and their geometric implications. Correctly analyzing these conditions leads to a clearer understanding of vector angles.
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Homework Statement



If a and b are vectors such that|a|=|b|=|a-b|, what is then the angle between a and b? What changes for |a|=|b|=|a+b|


Homework Equations





The Attempt at a Solution



|a|=|b| ⇔ a=b ∴ a=b ⇔|a-b|=0 ...identity of discernibles

angle between them is then 0.

|a|=|b|=|a+b| ⇔ |a+b| = |2a| or |2b| = |2||a| = 2|a|.

The magnitude of a or b changes but angle between a and b is 0 since a=b.

Is this correct logic?
 
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No, it's not. |a|=|b| doesn't imply a=b. For example, |(1,0)| = |(0,1)|.
 

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