A ray of light comes along the line L and strikes the plane mirror kept along the plane P at B, A(2,1,6) is a point on the line L,whose image about P is  $A\text{'}$. It  is given that L is  $\frac{x-2}{3}=\frac{y-1}{4}=\frac{z-6}{5}$   and P is  $x+y-2z=3.$ Then, which of the following is (are) true ?

Let  $A\text{'}(x_2,y_2,z_2)$  be th image of  $A(2,1,6,)$ about mirror  $x+y-2z=3.$  Then,
 $\frac{x_2-2}{1}=\frac{y_2-1}{1}=\frac{z_2-6}{-2}=\frac{-2(2+1-12-3)}{1^2+1^2+{(-2)}^2}=4$
 $\Rightarrow (x_2,y_2,z_2)=(6,5,-2)$
$\therefore$  The coordinates of  $A\text{'}$  are  $(6,5,-2)$
let  $\frac{x-2}{3}=\frac{y-1}{4}=\frac{z-6}{5}=5$
$x=2+3\lambda ,y=1+4\lambda ,z=6+5\lambda ,$   lies on plane 
 $$\begin{gathered} x+y-2z=3 \\ \Rightarrow 2+3\lambda +1+4\lambda -2(6+5\lambda )=3 \\ \Rightarrow \lambda =-4 \end{gathered}$$
$\therefore$   The coordinates of B are (-10,-15,-14)