Question

If the shortest distance between the lines $\bar{r}_1 = \alpha\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k}), \lambda \in \mathbb{R}, \alpha > 0$ and $\bar{r}_2 = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k}), \mu \in R$, is $9$, then the value of $\alpha$ is

• A. 4
• B. 6
• C. 8
• D. 3

Hint:

Cross product of direction vectors gives the vector perpendicular to both lines, which is used for shortest distance.

Answer 1

The Correct Option is B