Constructing a straight line intersecting four lines

In this paper, we determine the set S of straight lines L0 that have intersections with four given distinct lines L1, ... , L4 in R3. If any two of the four given lines are skew, i.e., not coplanar, 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 L0 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 L0 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. (c) 2023 Elsevier Inc. All rights reserved.