Formula for 3D Rotation

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This Demonstration explains a formula for the rotation of the vector around the axis given by the unit vector through the angle .

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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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Contributed by: Izidor Hafner (September 2011)
Open content licensed under CC BY-NC-SA


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