Distances between Points, Lines and Planes.
Distance between two Points:
Given A(2|1|-7), B(5|5|5) Distance between A and B : ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ d(A,B) = 13
It's calculated by the Pythagorean formula.
d = √( (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2)
Distance between a point and a line:
Given P(2|0|3) −> ⎧ 1 ⎫ ⎧ 1 ⎫ g : x = ⎪ 1 ⎪ + s·⎪ 0 ⎪ ⎩ 0 ⎭ ⎩-2 ⎭ Distance between P and g: ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ d(P,g) = 2,4494897
Take the plane E in normal form with the point P as position vector and the direction of the line g as normal vector. Determine the point of intersection point S between this plane and the line g. The distance between S and P is the distance between the point and the line.
Distance between Point and Plane:
Given P(0|0|0) E : x + y = 1 Distance between P and E : ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ d(P,E) = -0,70710678
Intersect the plane by the perpendicular from the point to the plane and determine the distance between the point of intersection and the given point.