Which of the following matrix equation is correct for 3 D rotation around z axis?
Posted: Thu Jul 14, 2022 8:45 am
a) \(\begin{matrix}x1 & sinθ \; -cosθ \; 0 \; 0 & x0\\
[ y1 ] = & [ cosθ \; sinθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)
b) \(\begin{matrix}x1 & cosθ \; -sinθ \; 1 \; 1 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 1 \; 1 ] &[ y0 ]\\
z1 & 0 \; 0 \; 0 \; 1 & z0\\
1 & 0 \; 0 \; 1 \; 0 & 1\end{matrix}
\)
c) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
0 & 1 \; 1 \; 1 \; 0 & 0\end{matrix}
\)
d) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)
[ y1 ] = & [ cosθ \; sinθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)
b) \(\begin{matrix}x1 & cosθ \; -sinθ \; 1 \; 1 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 1 \; 1 ] &[ y0 ]\\
z1 & 0 \; 0 \; 0 \; 1 & z0\\
1 & 0 \; 0 \; 1 \; 0 & 1\end{matrix}
\)
c) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
0 & 1 \; 1 \; 1 \; 0 & 0\end{matrix}
\)
d) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)