You are given a points (x1, y1, z1) and a plane a * x + b * y + c * z + d = 0. The task is to find the perpendicular(shortest) distance between that point and the given Plane.
Input: x1 = 4, y1 = -4, z1 = 3, a = 2, b = -2, c = 5, d = 8
Output: Perpendicular distance is 6.78902858227
Input: x1 = 2, y1 = 8, z1 = 5, a = 1, b = -2, c = -2, d = -1
Output: Perpendicular distance is 8.33333333333
Approach: The perpendicular distance (i.e shortest distance) from a given point to a Plane is the perpendicular distance from that point to the given plane. Let the co-ordinate of the given point be (x1, y1, z1)
and equation of the plane be given by the equation a * x + b * y + c * z + d = 0, where a, b and c are real constants.
The formula for distance between a point and Plane in 3-D is given by:
Distance = (| a*x1 + b*y1 + c*z1 + d |) / (sqrt( a*a + b*b + c*c))
Below is the implementation of the above formulae:
Perpendicular distance is 6.78902858227
- Shortest distance between a Line and a Point in a 3-D plane
- Mirror of a point through a 3 D plane
- Hammered distance between N points in a 2-D plane
- Find mirror image of a point in 2-D plane
- Find the foot of perpendicular of a point in a 3 D plane
- Find foot of perpendicular from a point in 2 D plane to a Line
- Number of jump required of given length to reach a point of form (d, 0) from origin in 2D plane
- Shortest distance between a point and a circle
- Perpendicular distance between a point and a Line in 2 D
- Optimum location of point to minimize total distance
- Find the minimum sum of distance to A and B from any integer point in a ring of size N
- Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles
- Ratio of the distance between the centers of the circles and the point of intersection of two direct common tangents to the circles
- Count paths with distance equal to Manhattan distance
- Reflection of a point at 180 degree rotation of another point
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.