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

[patrickmoloney]

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?

 

[vela]

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