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## Main Question or Discussion Point

imagine we rotate a vector centered at the origin with euler angles alpha,beta,gamma.

now the question is, can we do this rotation by the means of defining a vector N(which its lenght is 1).and rotating the vector zeta radians counter clockwise around N?

I think it must be possible and I want to know if N is unique(we have only one N for the given euler angles) and I want to find N and zeta in terms of alpha beta and gamma.

thank you.(complete answers really apreciated!!GOD bless those who give complete anwers!!)

P.S: what I've done to find the answer:I used cartesian coordinates and found the rotatian matrix correspending to a rotation zeta over a given N.>>RA=A'

I found R.A is a column matrix (x,y,z) and A'(x',y',z').and R is a 3x3 matrix which I found in terms of N(nx,ny,nz) and zeta.

now the question is, can we do this rotation by the means of defining a vector N(which its lenght is 1).and rotating the vector zeta radians counter clockwise around N?

I think it must be possible and I want to know if N is unique(we have only one N for the given euler angles) and I want to find N and zeta in terms of alpha beta and gamma.

thank you.(complete answers really apreciated!!GOD bless those who give complete anwers!!)

P.S: what I've done to find the answer:I used cartesian coordinates and found the rotatian matrix correspending to a rotation zeta over a given N.>>RA=A'

I found R.A is a column matrix (x,y,z) and A'(x',y',z').and R is a 3x3 matrix which I found in terms of N(nx,ny,nz) and zeta.