What is the shortest distance between skew lines in 3D space?
Answer (1)
The shortest distance between skew lines (lines that are not parallel and do not intersect) is the perpendicular distance between them. To find it, we first find two points, one on each line, say P 1 on line 1 and P 2 on line 2 . Next, we compute the vector between these two points, P 1 P 2 . The shortest distance is given by the formula:
D = |(P 1 P 2 ) · (d 1 × d 2 )| / |d 1 × d 2 |
where d 1 and d 2 are the direction vectors of the two lines, and d 1 × d 2 gives a vector perpendicular to both lines. This distance represents the shortest path between the two skew lines.
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