## 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 =
√( (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} + (z_{1} - z_{2})^{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