If a particle moving along $x-2 y-3=0$ gets reflected in a perpendicular direction upon hitting the line $3…
If a particle moving along $x-2 y-3=0$ gets reflected in a perpendicular direction upon hitting the line $3 x-2 y-5=0$, then the line of the movement of the particle after reflection is
$2 x+y+1=0$
$2 x+y-1=0$
$2 \mathrm{x}+\mathrm{y}-3=0$
$2 x+y+3=0$
Solution
Given line in $x-2 y-3=0$ which reflected by the line $3 \mathrm{x}-2 \mathrm{y}-5=0$.
Let the slope of reflected ray in $\mathrm{m}^1$
$
2 \mathrm{y}=\mathrm{x}-3
$
$
y=\frac{1}{2} x-\frac{3}{2}
$
$
\mathrm{m}_1=\frac{1}{2}
$
As inclined ray and reflected ray are normal to each other then, $\mathrm{mm}^1=-1$.
So, $\mathrm{m}^1=-2$.
Intersection of two lines $x-2 y-3=0$ and $3 x-2 y-5$ $=0$ is $(1,-1)$.
Required equation of line $=(y+1)=-2(x-1)$
$
\Rightarrow 2 \mathrm{x}+\mathrm{y}-1=0
$