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