Geometry 3D

Line throught two Points

Two points determine a straight line. Its equation is formed and its position to the co-ordinate planes is analysed.

Example:

Line through  A(1|1|1), B(2|5|6)

Parametric representation
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  ->  ⎧ 1 ⎫     ⎧ 1 ⎫
  x = ⎪ 1 ⎪ + t·⎪ 4 ⎪
      ⎩ 1 ⎭     ⎩ 5 ⎭

Distance from origin
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  d = 0,78679579

Position to the xy plane
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
 Orthogonal projection:  4·x - y = 3
 Point of intersection:  S1(0,8|0,2|0)
 Angel of intersection:  50,490288°

Position to the yz plane
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
 Orthogonal projection:  5·y - 4·z = 1
 Point of intersection:  S2(0|-3|-4)
 Angel of intersection:  8,8763951°

Position to the xz plane
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
 Orthogonal projection:  5·x - z = 4
 Point of intersection:  S3(0,75|0|-0,25)
 Angel of intersection:  38,112927°
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