Question

A ray of light comes along the line $L=0$ and strikes the plane mirror kept along the plane $P=0$ at $B$. $A(2,1,6)$ is a point on the line $L=0$ whose image about $P=0$ is $A^{\prime }$. It is given that $L=0$ is $\frac{x-2}{3}=\frac{y-1}{4}=\frac{z-6}{5}$ and $P=0$ is $x+y-2z=3$.

The coordinates of $B$ are

• A. $(5,10,6)$
• B. $(10,15,11)$
• C. $(-10,-15,-14)$
• D. None of these

Answer 1

The correct option is C $(-10,-15,-14)$

Let $\frac{x-2}{3}=\frac{y-1}{4}=\frac{z-6}{5}=\lambda$
$x=2+3\lambda ,y=1+4\lambda ,z=6+5\lambda$ lies on plane $x+y-2z=3$
$\Rightarrow 2+3\lambda +1+4\lambda -2(6+5\lambda )=3$ $\Rightarrow \lambda =-4$

Point $B\equiv (-10,-15,-14)$