Which of the following statements are correct?
(A) Two skew lines lie in the same plane.
(B) If two lines intersect, the shortest distance between them is zero.
(C) The distance between two parallel lines is the length of the perpendicular drawn from a point on one line to the other line.
(D) Two distinct lines whose direction ratios are proportional are skew lines.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (C) only
Two lines in space are of three kinds: intersecting, parallel, or neither. Lines that are neither parallel nor intersecting are skew lines; they do not lie in one plane.
Lines with proportional direction ratios are parallel. Parallel lines always lie in one plane, and the distance between them is the perpendicular distance from a point of one line to the other.
So skew lines are non-coplanar, intersecting lines are at distance 0, and lines with proportional direction ratios are parallel.
Checking the statements
(A) Two skew lines lie in the same plane — Incorrect. Skew lines are non-coplanar.
(B) If two lines intersect, the shortest distance between them is zero — Correct. The common point is on both lines.
(C) The distance between two parallel lines is the length of the perpendicular drawn from a point on one line to the other line — Correct. This is the distance between parallel lines.
(D) Two distinct lines whose direction ratios are proportional are skew lines — Incorrect. Proportional direction ratios make the lines parallel, not skew.