Let $L:{\mathbb R}^3 \to {\mathbb R}^3$ be the reflection with respect to the plane spanned by $\lbrace \left[\begin{array}{c} -2\cr 8\cr 7 \end{array}\right],\left[\begin{array}{c} 2\cr 4\cr 5 \end{array}\right] \rbrace$. Find the matrix of $L$. Hint: First find the matrix $[L]_B^B$ in a basis that contains the two given vectors and their crossed product. Then use transition matrices.
$[L]$ = $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$