Question

Find the shortest distance between the given lines. 

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

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,

= 6 + 60 – 4

= 62

Therefore, the shortest distance between the given lines is