What Are the Steps to Calculate Euler's Angles for Rotating a Vector?

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To calculate Euler's angles for rotating a vector, one must identify the specific rotation sequence, such as zyz, and determine the angles alpha, theta, and gamma. The user is attempting to rotate a vector from (0,0,15) to (3,-12,15) and is struggling with the angle calculations after the initial rotation in the x-y plane. It is suggested to use quaternion to Euler conversion methods, which can be found in various online resources. The focus should remain on the orientation of the vector rather than scaling factors. Accurate calculations can be achieved by following established quaternion conversion algorithms.
theboss2012
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Hello,

I have read about Euler's angles and matrices, including zxz,zyz, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma in the specific matrix. For example, I have a vector from the centre with vertex x,y,z of (0,0,15), I want to rotate it to (3,-12,15), what angles should I use or how can I obtain these angles ?

If let's say I choose zyz, i am finding difficulties finding the corresponding angles after the first x-y plane rotation.

Please disregard the scaling factor and just consider the orientation.

Look forward to hearing from you
 
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