MatheAss 9.0Geometry 3D

Intersection of Plane and Line

Given a plane and a line, the intersection point and the intersection angle are calculated.

The plane may be entered in parametric representation or as coordinate equation, the line in parametric representation or by two points.

Example 1:

Plane E :
¯¯¯¯¯¯¯¯¯
  E : x + y + z = 5

Line g :
¯¯¯¯¯¯¯¯
      ->  ⎧ 5 ⎫     ⎧ 0 ⎫
  g : x = ⎪ 0 ⎪ + r·⎪ 1 ⎪
          ⎩ 0 ⎭     ⎩ 1 ⎭

Intersection point :
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  S(5|0|0)

Intersection angle :
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  α = 54,73561°

Example 2:

Plane E :
¯¯¯¯¯¯¯¯¯
  E : 2·x + 8·y − 5·z = 0

Line g :
¯¯¯¯¯¯¯¯
      ->  ⎧ 2 ⎫     ⎧ 1 ⎫
  g : x = ⎪ 0 ⎪ + r·⎪ 1 ⎪
          ⎩ 3 ⎭     ⎩ 2 ⎭

E and g are parallel
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  d(g,E) = -1,1406469

The diagram can be rotated with the left mouse button and be zoomed with the right mouse button.

See also:

Graphics 3D
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