Find the shortest distance between the lines whose vector equations are r=(i+2j+3k) μ(i-3j+2k) and r=4i+5j+6k+u(2i+3j+k)

Question

Find the shortest distance between the lines whose vector equations are

vector r=(i+2j+3k) λ(i-3j+2k) and vector r=4i+5j+6k+μ(2i+3j+k)

Answer 1

It is known that the shortest distance between the lines, The given lines are given by,

Substituting all the values in equation (1), we obtain

Therefore, the shortest distance between the two given lines is 3/√3 units.