Suppose I have three axis of rotation vectors $\vec{v_1},\vec{v_2},\vec{v_3}$ and angle of rotation as vectors $\theta_1,\theta_2,\theta_3$.
- Take a vector $P$ then apply rotation around $\vec{v_1}$ with rotation angle $|\theta_1|$
- From new orientation of $P$ apply rotation around $\vec{v_2}$ with rotation angle $|\theta_2|$
- From new orientation of $P$ apply rotation around $\vec{v_3}$ with rotation angle $|\theta_3|$
- Now you get final orientation of $P$
Question
- Shall we get the same orientation of P if rotate around resultant of $\vec{v_1},\vec{v_2},\vec{v_3}$ let us call V with an angle which is equal to the magnitude of the resultant of $\theta_1,\theta_2,\theta_3$.