Vector Normal to a Plane

The Unit Vector Normal to a Plane calculator computes the normal unit vector to a plane defined by three points in a three dimensional cartesian coordinate frame.

INSTRUCTIONS: Enter the following:

• (P1) Point 1 (e.g. 2,3,4)
• (P2) Point 2 (e.g. 5,6,7)
• (P3) Point 3 (e.g. 1,8,9)

Normal Unit Vector to the Plane (V): The calculator returns the vector normal to the plane defined by the three points.

NOTE: Positions in 3D and vectors are entered via comma  separate strings  (e.g. 4,12,-2).

The Math / Science

To compute the normal vector to a plane created by three points:

1. Create three vectors (A,B,C) from the origin to the three points (P1, P2, P3) respectively.
2. Using vector subtraction, compute the vectors U = A - B and W = A - C
3. Compute the vector cross product, V = U x W
4. Compute the unit vector of V,  `hatV = vecV/(|vecV|)`  

`hatV` is the unit vector normal to the plane created by the three points.

3D Vector Functions

• k⋅V - scalar multiplication
• V/k - scalar division
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• V x U • W - Computes the mixed product of three vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• Vector Components 3D - Returns a vector's magnitude, unit vector, spherical coordinates, cylindrical coordinates and angle from each axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
• (x,y) to (r, θ) - Cartesian to Polar
• (r, θ) to (x,y) - Polar to Cartesian 
• Vector Normal to a Plane Defined by Three Points