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 .
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 .

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