Rotate vector by a random little amountSuppose there is a vector v = ( v x , v y , v z )I want to rotate this vector by a random little amount (let's say at most 10 º ). How can I do that?

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Rotate vector by a random little amountSuppose there is a vector   v  =  (      v    x    ,      v    y    ,      v    z    )I want to rotate this vector by a random little amount (let&#039;s say at most   10      º   ). How can I do that?

Quinn Everett · Accepted Answer

Step 1Find two mutually perpendicular unit vectors       u    1   and       u    2   that are also perpendicular to your vector vThus the vectors       u    1    ,      u    2    ,            v              ‖        v        ‖             form an orthonormal basis for             R        3  . Let the rotation matrix R be defined as follows:  R  =      [          u      1        ,          u      2        ,                  v                  ‖          v          ‖                      ]  Then vectors x in             R        3   are expressed in this basis as y as follows  x  =  R  yNote that the y corresponding to your vector v is  y  =      [                            0                                      0                                      ‖          v          ‖                      ]  Now using spherical coordinates, we can express your desired vector as  y  =  r      [                            sin          ⁡          θ          cos          ⁡          ϕ                                      sin          ⁡          θ          sin          ⁡          ϕ                                      cos          ⁡          θ                      ]  where from the conditions of the problem   0  ≤  θ  ≤      10    ∘   and   ϕ is arbitrary. And   r  =  ‖  v  ‖.And finally the new vector in the world coordinates is given by  x  =  R  y

Rotate vector by a random little amount Suppose there is a vector v = ( v x

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