Question

The lines $\overline{r}=\hat{i}-\hat{j}+\lambda (2\hat{i}+\hat{k})$ and $r=(2\hat{i}-\hat{j})+\mu (\hat{i}+\hat{j}-\hat{k})$ intersect for

• A. $\lambda =1,\mu =1$
• B. $\lambda =2,\mu =3$
• C. All values of $\lambda$ and $\mu$
• D. No values of $\lambda$ and $\mu$

Answer 1

The correct option is A $\lambda =1,\mu =1$

$\overline{r}=\hat{i}-\hat{j}+\lambda (2\hat{i}+\hat{k})$

$\overline{r}=(2\hat{i}-\hat{j})+\mu (\hat{i}+\hat{j}-\hat{k})$

For the lines to intersect,

$1+2\lambda =2+\mu ;$

$-1=-1+\mu ;$

$\lambda =-\mu ;$

No value of $\lambda$ & $\mu$ satisfies all the three equations.

$\therefore$ The lines do not intersect.