Question

Find the shortest distance between the lines x- 1/2 = y - 2 / 3 = z - 3 / 4 ; x - 2 / 3 = y - 4 / 4 = z - 5 / 5

Answer 1

According to question

x1 - 1/2 = y1 - 2/3 = z1 - 3/4
Let it be equal to 0

Thus
x1 = 1/2
y1 = 2/3
z1 = 3/4

Similarly

x2 = 2/3
y2 = 1
z2 = 1

Thus distance = root [ x2-x1^2 + y2 - y1^2 + z2 - z1^2 ]
                        = root [ 1/36 + 1/9 + 1/16 ]
                        = root [ 29/144 ]
                        =  root 29 / 12