Question

Equation of the plane which contains the line $L:\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{2}$ and its image about the plane $x+y+z=3$

• A. $x=z$
• B. $x-2y+z=0$
• C. $x+z=0$
• D. $y=z$

Answer 1

The correct option is A $x=z$

The plane which contains the line $L:\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{2}$ and its image will always perpendicular to the mirror plane
$\therefore$ Direction ratio's of the required plane is
$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 2\\ 1& 1& 1\end{array}\right|=\hat{i}-\hat{k}$
So the equation of the plane is $x-z=d$
Point $(1,1,1)$ lies on the plane
$\therefore 1-1=d\Rightarrow d=0$
So equation of the plane $x=z$