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:
- Accepts a three dimensional vector with X, Y and Z components of vector (V),
- Calculates the magnitude of the vector |V|,
- 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
