Constructing a straight line intersecting four lines.

In this paper, we determine the set S of straight lines L 0 that have intersections with four given distinct lines L 1 , ... , L 4 in R 3. If any two of the four given lines are skew, i.e., not co-planar, Bielinski and Lapinska used techniques in projective geometry to show that there are either zero, one, or two elements in the set S. Using linear algebra techniques, we determine S and show that there are no, one, two or infinitely many elements L 0 in S , where the last case was overlooked in the earlier paper. For the sake of completeness, we provide a comprehensive determination of all the elements L 0 in S if at least two of the four given lines are co-planar. In this scenario, there may also be zero, one, two, or infinitely many solutions. [ABSTRACT FROM AUTHOR]