Let $X$ be a quasi-inner product space (\cite{sedam}), and 

$x,y \in X \backslash \{0\}$. We resolve the problem of 

the relations between the three vectors: so-called 

$g$-orthogonal projection of the vector $y$ on the 

subspace $[x]\;\;(-a(x,y)x, {\rm Lemma\;2})$, 

the best approximation of the vector $y$ with vector 

from $[x]\;\;(-b(x,y)x, {\rm Lemma\;1})$ and the 

vector $-\displaystyle\frac{g(x,y)}{\norm{x}\norm^{2}}x$. 

The equality 



\[

a(x, y) = b(x, y) = - \frac{g(x,y)}{\norm{x}\norm^{2}}

\;,

\]



\noindent is valid if and only if $X$ is an inner-product space 

(i.p. space)\footnote{If $X$ is a i.p. space then the vector 

$-\frac{g(x,y)}{\norm{x}^{2}}x$ is the ortogonal projection of 

the vector $y$ to the vector $x$.}.