V3 - Unit Vector

The Unit Vector calculator, U = V/|V|, computes the unit vector (U) for a vector (V) in Euclidean three dimensional space.

INSTRUCTIONS:  Enter the following:

• (V): Vector V
• (n): Round to this many digits.

Unit Vector (U): The calculator returns the unit vector (U).

The Math / Science

To compute the Unit Vector, this calculator:

1. Accepts a three dimensional vector with X, Y and Z components of vector (V),
2. Calculates the magnitude of the vector |V|,
3. Uses scalar multiplication to divide each of the vectors components by the magnitude. 

The result is a vector (U) that points in the same direction as the original vector (V), but with a magnitude of one.

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

References

• Light and Matter by Benjamin Crowell, Chapter 7.1 Vector Notation