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Shortest Distance Between Point and Plane Calculator

Calculates the shortest distance in space between given point and plane equation.

Calculator

Enter the point(coordinates)

Enter the equation of the plane

In 3D geometry, the shortest distance between a point and a plane is always the length of the perpendicular segment dropped from the point to the plane. This is a vital calculation in fields ranging from computer graphics (collision detection) to architectural engineering.

Plane (π) Foot (Q) Point P(x₁, y₁, z₁) d

The distance from a point to a plane is equal to length of the perpendicular lowered from a point on a plane.

If Ax + By + Cz + D = 0 is a plane equation, then distance from point P(Px , Py , Pz) to plane can be found using the following formula:

The distance from a point to a plane(d) = (APx + BPy + CPz + D)/ √(A+ B2 + C2)

Shortest Distance Between Point and Plane

Shortest Distance from a Point to a Plane

In 3D geometry, the shortest distance between a point and a plane is always the length of the perpendicular segment dropped from the point to the plane. This is a vital calculation in fields ranging from computer graphics (collision detection) to architectural engineering.

Step-by-Step Breakdown

  1. Standardize the Equation: Ensure your plane equation is in the form $Ax + By + Cz + D = 0$.
  2. Substitute the Coordinates: Plug the point $(x_1, y_1, z_1)$ into the plane equation.
  3. Absolute Value: Take the absolute value of the numerator (distance cannot be negative).
  4. Magnitude of Normal: Divide by the magnitude of the normal vector n⃗ = (A, B, C).
Quick Fact: If the result of your calculation is 0, it means the point lies exactly on the plane.