V3 - Vector Projection

vCalc Reviewed
Equation / Last modified by AndrewBudd on 2018/10/12 16:03
`W = `
Copied from
vCalc.V3 - Vector Projection

The Vector Projection calculator computes the resulting vector (W)  that is a projection of vector V onto vector U in three dimensional space.V3 Projection.png Vector V projected on vector U

INSTRUCTIONS: Enter the following:

  • (V): Enter the x, y and z components of V separated by commas (e.g. 3,4,2)
  • (U): Enter the x, y and z components of U separated by commas (e.g. 3,4,2)

Vector Projection: The calculator returns the projection of V onto U (W) in comma separated form.

The Math / Science

To compute the projection of vector V onto vector U:

  1. Compute the magnitude of vector V
  2. Compute angle between vectors V and U
  3. Compute the unit vector of vector U
  4. Compute the scalar (k) associated with the projection which is the magnitude of V times the cosine of the angle between them.
  5. Compute the vector resulting in the scalar multiplication of the unit vector of U and the scalar (k).

3D Vector Functions