Given A(2|1|-7), B(5|5|5) Distance between A and B : ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ d(A,B) = 13
It's calculated by the formula of Pythagoras.
d = √( (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2)
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 S between this plane and the line g. The distance between S and P is the distance between the point and the line.
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.