Distance between two hyperplanes xiao cosmo zhang september 9, 2014 suppose we have two parallel hyperplanes l 1. The distance between two planes is the shortest distance between the surfaces of the planes. Specifically, i want to determine if two planes are the same. If the line intersects the plane obviously the distance between them is 0. If we select an arbitrary point on either plane and then use the other planes equation in the formula for the distance between a point and a plane, then we will have obtained the distance between both planes. Suppose there are n atoms in the lattice, n1 atoms in a lattice plane. If n x dand n x e are two parallel planes, then their distance is e. The trick here is to reduce it to the distance from a point to a plane. The distance between two planes is equal to length of the perpendicular distance a one plane to another plane. If they are parallel, then find a point x1,y1 on the line and calculate the length of the. Angle between planes two planes that intersect form an angle, sometimes called a dihedral angle. Distance between a straight line and a plane in space. Given the equations of two non parallel planes, we should be able to determine that line of intersection.