JEE Main & Advanced Mathematics Matrices Matrices of Rotation of Axes

Matrices of Rotation of Axes

Category : JEE Main & Advanced

 We know that if \[x\] and \[y\] axis are rotated through an angle \[\theta \] about the origin the new coordinates are given by

 

\[x=X\,\cos \theta -Y\sin \theta \] and \[y=X\sin \theta +Y\cos \theta \]

 

\[\Rightarrow \left[ \begin{matrix} x  \\ y  \\ \end{matrix} \right]=\left[ \begin{matrix} \cos \theta  & -\sin \theta   \\ \sin \theta  & \cos \theta   \\ \end{matrix} \right]\,\left[ \begin{matrix} X  \\ Y  \\ \end{matrix} \right]\Rightarrow \left[ \begin{matrix} \cos \theta  & -\sin \theta   \\ \sin \theta  & \cos \theta   \\ \end{matrix} \right]\]

 

is the matrix of rotation through an angle \[\theta \].

 

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