# The lines $\overrightarrow{r}=(\widehat{i}-\widehat{j})+l(2\widehat{i}+\widehat{k})$ and $\overrightarrow{r}=(2\widehat{i}-\widehat{j})+m(\widehat{i}+\widehat{j}-\widehat{k})$ Option: 1 do not intersect for any values of l and m Option: 2 intersect for all values of l and m Option: 3 intersect for the values when l=2 and  Option: 4 intersect for the values when l=2 and m=2

$\overrightarrow{r}=(\widehat{i}-\widehat{j})+l(2\widehat{i}+\widehat{k})$

$=(2l+1)\widehat{i}-\widehat{j}+l\;\widehat{k}$

$\overrightarrow{r}=(2\widehat{i}-\widehat{j})+m(\widehat{i}+\widehat{j}-\widehat{k})$

$=(m+2)\widehat{i}+(m-1)\widehat{j}-m\widehat{k}$

For intersection

$\\1+2 \ell=2+\mathrm{m}\qquad\ldots(i)\\ -1=m-1\qquad\quad\ldots(ii)\\ \ell=-\mathrm{m}\qquad\qquad\quad\ldots(iii)\\ \text {from (ii) } m=0$

$\text {from (iii) } \ell=0$

These values of m and l do not satisfy equation (1). Hence the two lines do not intersect for any values of l and m

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