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# V3 - Vector Rotation

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Equation / Last modified by AndrewBudd on 2018/10/12 16:02
`V' = `

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vCalc.V3 - Vector Rotation

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e2fac0fd-711a-11e6-9770-bc764e2038f2

The **Vector Rotation** calculator computes the resulting vector created by rotating a base vector (**V**) about a rotation vector (**U**) by an angle(**α**).

**INSTRUCTIONS:** Enter the following:

- (
**V**): Base vector (V) to be rotated. Enter the x, y and z components of V separated by commas (e.g. 3,9,1) - (
**U**): Rotation axis vector (U). Enter the x, y and z components of U separated by commas (e.g. 3,9,1) - (
**α**): Rotation angle. Enter the angle of rotation. The default is degrees but radians and other units are available.

**Rotated Vector (V'):** The calculator returns the resultant vector (V') in comma separated form.

#### The Math / Science

This formula uses quaternions to compute the resulting vector from the specified rotation. It uses the rotation of axis (U) and the rotation angle (α) to compute the quaternion of rotation(q). It then uses the quaternion formula as follows:

V' = q V q^{*}

where:

- V' is the rotated resultant vector.
- q is the quaternion of rotation
- q
^{*}is conjugate of the quaternion of rotation.

#### 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

- Light and Matter by Benjamin Crowell, Chapter 7.1 Vector Notation
- An Engineer's Approach to Quaternions* (Damon D. Ostrander October 1998) See Quaternions RevA.pdf (attached).

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

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**V3 - Vector Rotation**, is listed in 1 Collection.