If the lines given by $\bar{r}=2 \hat{\imath}+\lambda(\hat{\imath}+2 \hat{\jmath}+m \hat{k})$ and…
If the lines given by $\bar{r}=2 \hat{\imath}+\lambda(\hat{\imath}+2 \hat{\jmath}+m \hat{k})$ and $\bar{r}=\hat{\imath}+\mu(2 \hat{\imath}+\hat{\jmath}+6 \hat{k})$ are
perpendicular, then the value of $m$ is
$\frac{3}{2}$
$\frac{-3}{2}$
$\frac{2}{3}$
$\frac{-2}{3}$
Solution
Given lines are $\perp$ er and their d.r.s. are $(1,2, \mathrm{~m})$ and $(2,1,6)$
$\therefore \quad 1(2)+2(1)+m(6)=0$
$\therefore \quad 6 m=-4 \quad \Rightarrow m=\frac{-2}{3}$