A) \[I\cos \theta +J\sin \theta \]
B) \[I\,\sin \theta +J\,\cos \theta \]
C) \[I\cos \theta -J\sin \theta \]
D) \[-I\cos \theta +J\sin \theta \]
Correct Answer: A
Solution :
\[B=\left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} \cos \theta & 0 \\ 0 & \cos \theta \\ \end{matrix} \right]+\left[ \begin{matrix} 0 & \sin \theta \\ -\sin \theta & 0 \\ \end{matrix} \right]\] \[=\cos \theta \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]+\sin \theta \left[ \begin{matrix} 0 & 1 \\ -1 & 0 \\ \end{matrix} \right]\] \[=I\cos \theta +J\sin \theta \]
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