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

Question

Find the shortest distance between the lines \(\bar{r}\)= i + j + λ(2i – j + k) and \(\bar{r}\)= 2i + j – k + µ(3i – 5 j + 2k)

Answer 1

From the given lines we have

\(\bar{a_1}=i+j,\bar{b_1}=2i-j+k\)

\(\bar{a_2}=2i+j-k,\bar{b_2}=3i-5j+2k\)

\(\bar{a_2}-\bar{a_1}=i-k\)