Formula for 3D Rotation
This Demonstration explains a formula for the rotation of the vector around the axis given by the unit vector through the angle .[more]
The formula is , using the dot and cross product of vectors.
The resultant vector is .
The vector is the orthogonal projection of the vector onto the vector .
The vector is the result of the rotation of the vector around through the angle .
The vector is the orthogonal projection of onto .
is the orthogonal projection of onto .