6. Skew Lines Two straight lines in space are said to be skew lines, if they are neither parallel nor intersecting.
7. Shortest Distance If l1 and l2 are two skew lines, then a line perpendicular to each of lines 4 and 12 is known as the line of shortest distance.
If the line of shortest distance intersects the lines l1 and l2 at P and Q respectively, then the distance PQ between points P and Q is known as the shortest distance between l1 and l2.
8. The shortest distance between the lines
9. The shortest distance between lines r = a1 + λb1 and r = a2 + μb2 is given by
10. The shortest distance parallel lines r = a1 + λb1 and r = a2 + μb2 is given by
11. Lines r = a1 + λb1 and r = a2 + μb2 are intersecting lines, if( b1 * b2) *( a2 – a1) = 0.
12. The image or reflection( x, y, z) of a point( x1, y1, z1) in a plane ax + by + cz + d = 0 is given by