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# V3 - Unit Vector

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Equation / Last modified by AndrewBudd on 2018/10/12 15:42
`U = `

The **Unit Vector** calculator, **U = V/|V|**, computes the unit * Vector in three dimensions* vector (

**U**) for a vector (

**V**) in Euclidean three dimensional space.

**INSTRUCTIONS:** Enter the following:

- (V): Enter the x, y and z components of
**V**separated by commas (e.g. 8,2,5)

**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

- 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

This equation,

**V3 - Unit Vector**, is used in 2 calculators and 1 equation/constant.**Calculators**

**Equations and Constants **