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Q.
The reflection of the plane $2x-3y + 4z-3 = 0$ in the plane $r - y + z - 3 = 0$ is the plane
Three Dimensional Geometry
Solution:
Equation of required plane be obtained by using the fact : Reflec tion of $a'x+b'y+c'z+d'=0$ in the plane
$ax +by+cz+d=0$ is given by
$2 (aa' +bb'+cc') (ax+by +cz+d)$
$=(a^{2}+b^{2}+c^{2}) (a'x +b'y +c'z+d')$
$\Rightarrow 2 (2+3+4) (x-y+z-3) =3 (2x-3y+4z-3)$
$\Rightarrow 6 (x-y+x-3) =2x-3y+4z-3$
$\Rightarrow 4x-3y+2z -15 =0$