The shortest distance between the lines \(\displaystyle\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-4}{-1}\) and \(\displaystyle\frac{x-2}{1}=\frac{y+1}{-4}=\frac{z-4}{5}\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
At the point (2, −1, 4), every fraction in both equations is 0:
\(x-2 = 0,\quad y+1 = 0,\quad z-4 = 0\)
So both lines pass through (2, −1, 4).
Their direction ratios 3, 2, −1 and 1, −4, 5 are not proportional, so the lines are not the same line. Two different lines with a common point intersect, and the shortest distance between intersecting lines is 0.