The discussion clarifies that the line of intersection of two planes can be determined using the cross product of their normal vectors. The normal vector of a plane is defined as perpendicular to any line within that plane. Consequently, the cross product results in a vector that is perpendicular to both normal vectors, establishing its parallelism to the line of intersection, which exists within both planes. It is important to note that the cross product yields a direction vector, not a specific line in space.
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therefore lieing in both planes, therefore along the line of intersectionmathman said:The line of intersection lies in both planes. The normal to a plane is (by definition) perpendicular to any line in the plane. The cross product then gives you a line perpendicular to both normals,
so that it must be parallel to the line of intersection.
therefore lieing in both planes, therefore along the line of intersection