91影视

The graph of the line L is,

The reflection of vector $\stackrel{鈫�}{\mathrm{x}}$about the line L in ${\mathrm{鈩�}}^2$is,

${\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=2{\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)-\left(\stackrel{鈫�}{\mathrm{x}}\right)$

Therefore, the graph of the line T is,

The projection of a vector $\stackrel{鈫�}{\mathrm{x}}$onto $\stackrel{鈫�}{\mathrm{u}}$is,

$$\begin{gathered} {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left(\frac{\stackrel{鈫�}{\mathrm{x}}路\stackrel{鈫�}{\mathrm{u}}}{\mathrm{uu}}\right)\stackrel{鈫�}{\mathrm{u}} \\ \mathrm{Here}, \\ \stackrel{鈫�}{\mathrm{x}}=\left[\begin{array}{c}{\mathrm{x}}_1\\ {\mathrm{x}}_2\end{array}\right],\stackrel{鈫�}{\mathrm{u}}=\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right] \\ \mathrm{Thus},\mathrm{the}\mathrm{projection}\mathrm{is}, \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left(\begin{array}{c}\left[\begin{array}{c}{\mathrm{x}}_1\\ {\mathrm{x}}_2\end{array}\right]路\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right]\\ \left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right]路\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right]\end{array}\right)\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right] \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left(\frac{{\mathrm{肠辞蝉胃虫}}_1+{\mathrm{蝉颈苍胃虫}}_2}{{\cos }^2\mathrm{胃}+{\sin }^2\mathrm{胃}}\right)\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right] \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left({\mathrm{肠辞蝉胃虫}}_1+{\mathrm{蝉颈苍胃虫}}_2\right)\left[\begin{array}{c}\mathrm{肠辞蝉胃}\\ \mathrm{蝉颈苍胃}\end{array}\right] \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left[\begin{array}{c}\left({\mathrm{肠辞蝉胃虫}}_1+{\mathrm{蝉颈苍胃虫}}_2\right)\mathrm{肠辞蝉胃}\\ \left({\mathrm{肠辞蝉胃虫}}_1+{\mathrm{蝉颈苍胃虫}}_2\right)\mathrm{蝉颈苍胃}\end{array}\right] \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left[\begin{array}{c}\left({\cos }^2{\mathrm{胃虫}}_1+\mathrm{肠辞蝉胃}{\mathrm{蝉颈苍胃虫}}_2\right)\\ \left(\mathrm{肠辞蝉胃蝉颈苍胃}{\mathrm{x}}_1+{\sin }^2\mathrm{胃}\right)\end{array}\right] \\ {\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left[\begin{array}{cc}{\cos }^2\mathrm{胃}& \mathrm{肠辞蝉胃蝉颈苍胃}\\ \mathrm{肠辞蝉胃蝉颈苍胃}& {\sin }^2\mathrm{胃}\end{array}\right]\stackrel{鈫�}{\mathrm{x}} \end{gathered}$$

$$\begin{gathered} \mathrm{The}\mathrm{reflection}\mathrm{of}\mathrm{the}\mathrm{vector}\stackrel{鈫�}{\mathrm{x}}\mathrm{is}, \\ \mathrm{T}\left(\stackrel{鈫�}{\mathrm{x}}\right)={\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ \mathrm{Here},{\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=2{\mathrm{proj}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)-\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ {\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=2\left[\begin{array}{cc}{\cos }^2\mathrm{胃}& \mathrm{肠辞蝉胃蝉颈苍胃}\\ \mathrm{肠辞蝉胃蝉颈苍胃}& {\sin }^2\mathrm{胃}\end{array}\right]\left(\stackrel{鈫�}{\mathrm{x}}\right)-\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ {\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=2\left(\left[\begin{array}{cc}{\cos }^2\mathrm{胃}& \mathrm{肠辞蝉胃蝉颈苍胃}\\ \mathrm{肠辞蝉胃蝉颈苍胃}& {\sin }^2\mathrm{胃}\end{array}\right]-1\right)\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ {\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=2\left(\left[\begin{array}{cc}{\cos }^2\mathrm{胃}& \mathrm{肠辞蝉胃蝉颈苍胃}\\ \mathrm{肠辞蝉胃蝉颈苍胃}& {\sin }^2\mathrm{胃}\end{array}\right]-\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\right)\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ {\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left(\left[\begin{array}{cc}2{\cos }^2\mathrm{胃}-1& 2\mathrm{肠辞蝉胃蝉颈苍胃}\\ 2\mathrm{肠辞蝉胃蝉颈苍胃}& 2{\sin }^2\mathrm{胃}-1\end{array}\right]\right)\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ {\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left[\begin{array}{cc}\cos 2\mathrm{胃}& \sin 2\mathrm{胃}\\ \sin 2\mathrm{胃}& -\cos 2\mathrm{胃}\end{array}\right]\left(\stackrel{鈫�}{\mathrm{x}}\right) \end{gathered}$$

$$\begin{gathered} \mathrm{T}\left(\stackrel{鈫�}{\mathrm{x}}\right)={\mathrm{ref}}_{\mathrm{L}}\left(\stackrel{鈫�}{\mathrm{x}}\right) \\ \mathrm{T}\left(\stackrel{鈫�}{\mathrm{x}}\right)=\left[\begin{array}{cc}\cos 2\mathrm{胃}& \sin 2\mathrm{胃}\\ \sin 2\mathrm{胃}& -\cos 2\mathrm{胃}\end{array}\right]\left(\stackrel{鈫�}{\mathrm{x}}\right) \end{gathered}$$