Perpendicular through Two Lines in 3D
Visualisation of two lines, with the line perpendicular to each determined by the cross product of the direction vectors
Determining the perpendicular line to both original lines
The first line is through points A and B, with direction vector . The second line is through C and D, with direction vector . These direction vectors are also shown at the origin, along with their cross product.
The point E can be moved along the line AB, demonstrating a scalar multiple of the direction vector. The second line through E has the cross product as its direction vector. The point P can be moved along this line, representing a scalar multiple of the cross-product vector.
The point Q cab be moved along the line CD, representing a scalar multiple of its direction vector. When P matches Q, then the line segment EP = EQ represents the shortest segment between the two lines.