DC of line $\equiv \left(\frac{3}{\sqrt{m^2+10}},\frac{-m}{\sqrt{m^2+10}},\frac{1}{\sqrt{m^2+10}}\right)$

$Q\equiv \left(1+\frac{3r}{\sqrt{m^2+10}},-2+\frac{-mr}{\sqrt{m^2+10}},3+\frac{r}{\sqrt{m^2+10}}\right)$

$Q$ lies on $x+2y-3z+10=0$

$1+\frac{3r}{\sqrt{m^2+10}}-4-\frac{2mr}{\sqrt{m^2+10}}-9-\frac{3r}{\sqrt{m^2+10}}+10=0$

$\Rightarrow \frac{r}{\sqrt{m^2+10}}\left(3-2 m-3\right)=2$

$\Rightarrow \frac{r}{\sqrt{m^2+10}}\left(-2 m\right)=2$

$r^2{m}^2=m^2+10$

$\frac{7}{2}{ m}^2=m^2+10\Rightarrow \frac{5}{2}{ m}^2=10\Rightarrow m^2=4$

$\left|m\right|=2$