The Vector Projection calculator computes the resulting vector (W) that is a projection of vector V onto vector U in three dimensional space.
Vector V projected on vector U
INSTRUCTIONS: Enter the following:
- (V) Vector V
- (U) Vector U
Vector Projection (W): The calculator returns the vector in comma separated form.
The Math / Science
To compute the projection of vector V onto vector U:
- Compute the magnitude of vector V
- Compute angle between vectors V and U
- Compute the unit vector of vector U
- Compute the scalar (k) associated with the projection which is the magnitude of V times the cosine of the angle between them.
- Compute the vector resulting in the scalar multiplication of the unit vector of U and the scalar (k).
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
