  Let $\phi$ and $\phi'$ be two $\textrm{GL}(3)$ Hecke--Maass cusp forms. In
this paper, we prove that $\phi=\phi'\textrm{ or }\widetilde{\phi'}$ if there
exists a nonzero constant $\kappa$ such that $$L(\frac{1}{2},\phi\otimes
\chi_{8d})=\kappa L(\frac{1}{2},\phi'\otimes \chi_{8d})$$ for all positive odd
square-free positive $d$. Here $\widetilde{\phi'}$ is dual form of $\phi'$ and
$\chi_{8d}$ is the quadratic character $(\frac{8d}{\cdot})$. To prove this, we
obtain asymptotic formulas for twisted first moment of central values of
quadratic twisted $L$-functions on $\textrm{GL}(3)$, which will have many other
applications.
