Question

Choose correct alternatives :

The shortest distance between the lines ${\displaystyle \overrightarrow{r}=(\hat{i}+2\hat{j}+\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})\text{and}\overrightarrow{r}=(2\hat{i}-\hat{j}-\hat{k})+\mu (2\hat{i}+\hat{j}+2\hat{k})}$ is ______.

पर्याय

• ${\displaystyle \frac{1}{\sqrt{3}}}$

• ${\displaystyle \frac{1}{\sqrt{2}}}$

• ${\displaystyle \frac{3}{\sqrt{2}}}$

• ${\displaystyle \frac{\sqrt{3}}{2}}$

Answer 1

The shortest distance between the lines ${\displaystyle \overrightarrow{r}=(\hat{i}+2\hat{j}+\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})\text{and}\overrightarrow{r}=(2\hat{i}-\hat{j}-\hat{k})+\mu (2\hat{i}+\hat{j}+2\hat{k})}$ is ${\displaystyle \underline{\frac{3}{\sqrt{2}}}}$.