Finding the distance from a point to a plane

In this publication, we will consider what the distance from a point to a plane is, and by what formula it is calculated. We will also analyze an example of solving a problem on this topic.

Point-to-Plane Distance Calculation

To find the distance from an arbitrary point for any plane, you need to lower the perpendicular from it to this plane.

Perpendicular length (d) is the required distance.

Formula for calculating

Distance in XNUMXD space from a point O with coordinates (O_x, O_y, O_z) to the straight line given by the equation Ax + By + Cz + D = 0, is considered as follows:

Example of a problem

Let’s say we have a plane 3x – 4y + 2z – 5 = 0. Find the distance from it to the point O (2, 0, -6).

Decision:

Substituting in the formula above the known values ​​we get: