3. In the Cartesian coordinate system $x O y$, it is known that point $A(1,0)$, and point $B$ lies on the line $y=3x$. If $\triangle A O B$ is an isosceles triangle, then the coordinates of point $B$ are $\qquad$
3. $\left( \pm \frac{\sqrt{10}}{10}, \pm \frac{3 \sqrt{10}}{10}\right),\left(\frac{1}{5}, \frac{3}{5}\right),\left(\frac{1}{2}, \frac{3}{2}\right)$. Let $B(t, 3 t)(t \neq 0)$.
If $O A=O B$, then $\sqrt{t^{2}+(3 t)^{2}}=1$.
Thus, $t= \pm \frac{\sqrt{10}}{10}$.
Therefore, $B\left( \pm \frac{\sqrt{10}}{10}, \pm \frac{3 \sqrt{10}}{10}\right)$.
If $A B=O A$, then $\sqrt{(t-1)^{2}+(3 t)^{2}}=1$.
Thus, $t=\frac{1}{5}$.
Therefore, $B\left(\frac{1}{5}, \frac{3}{5}\right)$.
If $O B=B A$, then $t=\frac{1}{2}$.
Therefore, $B\left(\frac{1}{2}, \frac{3}{2}\right)$.