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 $A^{\prime }$ are

• A. $(6,5,2)$
• B. $(6,5,-2)$
• C. $(6,-5,2)$
• D. None of these

Answer 1

The correct option is B $(6,5,-2)$

Let $A^{\prime }(x_2,y_2,z_2)$ be the image of $A(2,1,6)$ about mirror $x+y-2z=3$. Then, $\frac{x_2-2}{1}=\frac{y_2-1}{1}=\frac{z_2-6}{-2}$ $=\frac{-2(2+1-12-3)}{1^2+1^2+2^2}=4$ $\Rightarrow (x_2,y_2,z_2)\equiv (6,5,-2)$.