Sum of vector product implies vectors are equal?

Question

Sorry, I'm new so my title definitely needs work.

Anyway I was wondering

If $$\sum x_i y_i = \sum y_i y_i$$ is true.

Does it imply that

$$x_i = y_i$$ ?

Answer 1

No this is not true. Take for example $y = (1,2)'$ and $x = (3,1)'$. Then both $y'y$ and $x'y$ are equal to 5, but $x\neq y$.