# Rotation about an axis by matrix multiplication

Suppose I have three axis of rotation vectors $\vec{v_1},\vec{v_2},\vec{v_3}$ and angle of rotation as vectors $\theta_1,\theta_2,\theta_3$.

1. Take a vector $P$ then apply rotation around $\vec{v_1}$ with rotation angle $|\theta_1|$
2. From new orientation of $P$ apply rotation around $\vec{v_2}$ with rotation angle $|\theta_2|$
3. From new orientation of $P$ apply rotation around $\vec{v_3}$ with rotation angle $|\theta_3|$
4. Now you get final orientation of $P$

Question

1. 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 $\theta_1,\theta_2,\theta_3$.
• What do you mean by "the resultant of $\theta_1,\theta_2,\theta_3$" ? Nov 11, 2014 at 19:01
• Means vector sum Nov 11, 2014 at 21:57
• But $\theta_1,\theta_2,\theta_3$ are not vectors. Nov 12, 2014 at 15:57
• They are angles represented by vectors..As explained in the question magnitude of this is the angle in radian Nov 13, 2014 at 1:22