A ray is sent along the line $\frac{x-0}{2}=\frac{y-2}{2}=\frac{z-1}{0}$ and is reflected by the plane x = 0 at a point A. The reflected ray is again reflected by the plane x+2y = 0 at point B. The initial ray and final reflected ray meets at point J then which of the following is/are true

Let the coordinates of the point(s) be $\left(x_1,y_1,z_1\right).$.

The equation of the line passing through $\left(x_1,y_1,z_1\right)$

with direction ratios 1, –5 and –2 is

$\frac{x-x_1}{1}=\frac{y-y_1}{-5}=\frac{x-x_1}{-2}$

This line is will intersect line $\frac{x}{1}=\frac{y+5}{1}=\frac{z+1}{1}$ if $\left|\begin{array}{ccc}1& -5& -2\\ 1& 1& 1\\ x_1& y_1+5& z_1+1\end{array}\right|=0$

$\Rightarrow x_1+y_1-2z_1+3=0 \left(i\right)$

Similarly

$\left|\begin{array}{ccc}1& -5& -2\\ 1& \frac{1}{3}& \frac{1}{2}\\ x_1+5& y_1& z_1\end{array}\right|=0$

$\Rightarrow 11x_1+15y_1-32z_1+55=0 \left(ii\right)$

(2,–3,1) is a point on the first line and satisfies the condition (i)
(1, 2, 3) is a point on the second line and satisfies the condtion (ii)