Find the distance between the lines `l_1`and `l_2`given by ` vec r= hat i+2 hat j-4k+lambda(2 hat i+3 hat j+6 hat k)`and ` vec r=3 hat i+3 hat j-5k+mu(2 hat i+3 hat j+6 hat k)`.

Explanation

To find the distance between the two parallel lines given by the equations:

1. \(\vec{r_1} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})\)
2. \(\vec{r_2} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})\)

we can use the formula for the distance \(d\) between two parallel lines:

\[
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