Question

Find the shortest distance between the given lines.

vectors r = (i + 2j - 4k) + λ(2i + 3j + 6k), r = (3i + 3j - 5k) + μ(-2i + 3j + 8k).

Answer 1

Given equations :

3. Shortest distance between two lines :

The shortest distance between the skew lines \(\vec r=\bar a_1+\lambda \bar{b_1}\) and

\(\vec r=\bar a_2+\lambda \bar {b_2}\) is given by,

For given lines,

= 12 – 28 + 0

= - 16

Therefore, the shortest distance between the given lines is