The lines\
$\overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\ell(2 \hat{\mathrm{i}}+\hat{\mathrm{k}})$ and
$\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})+\mathrm{m}(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$
Correct Option: 3,
$\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}(1+2 \ell)+\hat{\mathrm{j}}(-1)+\hat{\mathrm{k}}(\ell)$
$\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}(2+\mathrm{m})+\hat{\mathrm{j}}(\mathrm{m}-\mathrm{l})+\hat{\mathrm{k}}(-\mathrm{m})$
For intersection
$1+2 \ell=2+m$ ....(i)
$-1=m-1$ .....(ii)
$\ell=-\mathrm{m}$ .....(iii)
from (ii) $m=0$
from (iii) $\ell=0$
These values of $m$ and $\ell$ do not satisfy equation (1).
Hence the two lines do not intersect for any values of $\ell$ and $\mathrm{m}$.
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