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In this paper we give the solution for the following geometric problem. Given four arbitrarily placed lines in space, K, L, M, and N, find a fifth line V that intersects all four. And if there is more than one, find all of them. The author aims at an analytic solution and have developed some notation and basic tools for manipulating lines in projective 3-space; and used these tools on lines in space. And on the way to the solution, we encounter an interesting relationship between dimensions that is a useful tool for many other geometrical problems.