Inner products of of two vectors which are both orthogonal to a third vector.

Question

If, in an $R^n$ space,

$(x,y)=0$

$(x,z)=0$

Then what about $(z,y)$?

What if $(z,y)\approx 1$ (although z,y are two different vectors with different elements), then what can we say about y and z?

Is it a necessity that $(z,y)\approx 1$?

Answer 1

Suppose that $n=2$, that $x=(1,0)$, that $y=(0,1)$, and that $z=(0,t)$, for some real number $t$. Then $\langle x,y\rangle=\langle x,z\rangle=0$, but $\langle z,y\rangle=t$.