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`V = f( "P1" , "P2" , "P3" )`

Enter a value for all fields

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).

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

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

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

**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.**(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- Vector Normal to a Plane Defined by Three Points