Look at the plane equation in the box first. There are three lines in all. The first line is the numerator part of the straight line L 1, and the second line is the denominator part of the straight line L 1. (The real point (2, 1, 3) is the fixed point through which the straight line L 1 passes. The above two lines determine the straight line L 1. But the plane is not certain, because there are countless planes passing through the straight line L 1! So if you want to determine the unique plane, you need to introduce a straight line, or a straight line vector, that is, (-4,-1, 3), that is, S. The plane π determined by them must pass through L 1 and be parallel to S (because S is represented by a space vector).

If you want to know more, I suggest reading the textbook Spatial Analytic Geometry, which is very detailed.