$\text{ The lines }\overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+l(2\hat{\mathrm{i}}+\hat{\mathrm{k}})\text{ and }\overrightarrow{\mathrm{r}}=(2\hat{\mathrm{i}}-\hat{\mathrm{j}})+\mathrm{m}(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$

$\begin{array}{l}\overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{j})+l(2\overrightarrow{i}+\overrightarrow{k})\\ \overrightarrow{r}=(2\overrightarrow{i}-\overrightarrow{j})+m(\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})\\ solve the above equations , \\ \left[2l+1\right]\hat{i}-\hat{j}+l\hat{k}=\left[m+2\right]\hat{i}+\left[m-1\right]\hat{j}-m\hat{k}\\ \text{ Equate the coefficients of }i,j,k\\ 2l+1=m+2\Rightarrow 2l-m=1\to \left(1\right)\\ -1=-1+m\Rightarrow m=0\to \left(2\right)\\ \Rightarrow l=\frac{1}{2}\end{array}$

$\text{ Also }l=-m\text{ which is not true }$

$\text{ So, lines do not intersect }\Rightarrow \text{ option }4$