Question

The reflection of the plane $2x-3y+4z-3=0$ in the plane $r-y+z-3=0$ is the plane

• A. $4x-3y+2z-15=0$
• B. $x-3y+2z-15=0$
• C. $4x+3y-2z+15=0$
• D. None of these

Answer 1

Answer: (A)

Equation of required plane be obtained by using the fact : Reflec tion of $a^{\prime }x+b^{\prime }y+c^{\prime }z+d^{\prime }=0$ in the plane
$ax+by+cz+d=0$ is given by
$2(a{a}^{\prime }+b{b}^{\prime }+c{c}^{\prime })(ax+by+cz+d)$
$=(a^2+b^2+c^2)(a^{\prime }x+b^{\prime }y+c^{\prime }z+d^{\prime })$
$\Rightarrow 2(2+3+4)(x-y+z-3)=3(2x-3y+4z-3)$
$\Rightarrow 6(x-y+x-3)=2x-3y+4z-3$
$\Rightarrow 4x-3y+2z-15=0$