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