How to compute angle between vectors a and b if |a|=|b|=|a+b|

Question

How to compute angle between vectors a and b if |a|=|b|=|a+b|. This is everything I have. I start with formula $cos(\alpha)=\frac{ab}{|a| |b|}$.

Thank you for your help.

Answer 1

Sometimes a figure is worth a thousand words:

Answer 2

Since $|a+b|^2=\langle a+b,a+b \rangle = |a|^2 + 2\langle a, b \rangle + |b|^2$, it follows that $2\langle a,b \rangle=-|a|^2$. Hence $\cos(\alpha)= -\frac{1}{2}$.