Geometry 3D

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 formula of Pythagoras.

d = √( (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2)

Distance between Point and 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 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.

Distance between two Lines:

See Intersection of two Lines

Distance between Plane and Line:

See Intersection of Plane and Line

Distance between two Planes:

See Intersection of two Planes

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