2D and 3D Rotations

2D Rotations

Given $V=\left[\begin{array}{c}-4\\6\\1\end{array}\right]$ and $\theta=25^{o}$ then R=?? and V’=??
Given $V=\left[\begin{array}{c}3\-5\\1\end{array}\right]$ and $\theta=35^{o}$ then R=?? and V’=??

3D Rotations

Given Roll=10^o, Pitch=5^o, Yaw=12^o, and $V=\left[\begin{array}{c}3\\-4\\5\\1\end{array}\right]$ then R_z=??, R_x=??, R_y=??, R_zxV=??, R_xxV=??, R_yxV=??

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