Hi,

regarding the formula in https://bivector.net/3DPGA.pdf I have a question about distance between lines

The sheet mentions :

I’m a bit triggered by this \cosec \alpha here… I thought that the join of two lines already measured (roughly speaking) the signed distances between the lines measured along their common normal line.

Here it is as if the weight of the meet was proportional to the oriented perpendicular distance between the two lines but weighted by the sine of the angle between their relative directions.

Btw this formula will not work for distance between parallel lines, shouldn’t there be another one for this case implying something like the infinite norm of their wedge product ?