Available data
- The plane β which is defined by a normal vector n and point P.
- The vector v which lies on the surface of the plane.(the angle between v and n is 90 degrees).
- The angle α to which v should be rotated.
How to obtain the rotated vector(vrot) ?
Note that the vectors are 3D.
Best Answer
If $v \neq 0$ and $n$ is a unit vector, the vectors $v$ and $n \times v$ are an orthogonal basis of your plane, and the result of rotating $v$ counterclockwise (about $n$) by an angle $\alpha$ is $$ (\cos\alpha)\, v + (\sin\alpha)\, (n \times v). $$