Question

Find the shortest distance between the lines r = (4i - j) + λ(i + 2j - 3k) and r = (i - j + 2k) + μ(i + 4j - 5k)

Answer 1

We know that the shortest distance between the skew lines \(\bar{r} = \overline{a_1} + λ\overline{b_1}\) and \(\bar{r} = \overline{a_2} + μ\overline{b_2}\) is given by

∴ required shortest distance between the given lines \(=\left|\frac{-2}{2\sqrt{3}}\right| = \frac{1}{\sqrt{3}}\) units.