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# V3 - Vector Projection

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Equation / Last modified by AndrewBudd on 2018/10/12 16:03
`W = `

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vCalc.V3 - Vector Projection

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a7d7cd06-5030-11e7-9770-bc764e2038f2

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**): 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:

- 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).

- multiply a vector by a scalar
- divide a vector by a scalar
- add two vectors
- subtract two vectors
- compute the dot product of two vectors
- compute the cross product of two vectors
- compute the unit vector of a vector
- compute the magnitude of a vector
- project a vector onto another vector
- compute the angle between two vectors
- rotate a vector around an axis
- convert spherical coordinates into a vector
- convert a vector into spherical coordinates

#### References

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**V3 - Vector Projection**, is used in 1 calculator.**Calculators**