# V3 - Vector Rotation

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vCalc.V3 - Vector Rotation
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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:

#### References

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