Intersection of two Lines 3D
Given two lines the program computes their point of intersection, the angle of intersection and their distances from the origin.
The two lines may be given in parametric representation or by two points.
If they don't have any common point their distance and the feet of the common perpendicular are calculated.
Example:
-> ⎧ 5 ⎫ ⎧ 0 ⎫
g : x = ⎪ 0 ⎪ + r·⎪ 1 ⎪
⎩ 0 ⎭ ⎩ 1 ⎭
-> ⎧ 0 ⎫ ⎧ 1 ⎫
h : x = ⎪ 5 ⎪ + s·⎪ 0 ⎪
⎩ 0 ⎭ ⎩ 1 ⎭
Intersection point of g and h : S(5|5|5)
Intersection angle of g and h : 60°
Distances from origin :
d(O,g)=5 d(O,h)=5
Example with skew lines:
-> ⎧ 10 ⎫ ⎧ 0 ⎫
g : x = ⎪ 0 ⎪ + r·⎪ 1 ⎪
⎩ 0 ⎭ ⎩-1 ⎭
-> ⎧ 0 ⎫ ⎧ 1 ⎫
h : x = ⎪ 5 ⎪ + s·⎪ 0 ⎪
⎩ 0 ⎭ ⎩ 5 ⎭
Skew lines
Distance d(g,h)=10,584755
Common perpendicular feet
F1(10|2,963|-2,963)
F2(-0,18519|5|-0,92593)
The diagram can be rotated with the left mouse button and be zoomed with the right mouse button.