Question

The equation of obtuse angular bisector of the planes $x-2y+2z+3=0,3x-6y-2z+2=0$ is

• A. $12x-14y+z-11=0$
• B. $2x-4y+8z-5=0$
• C. $16x-32y+8z+27=0$
• D. $2x-4y-20z-15=0$

Answer 1

The correct option is D $2x-4y-20z-15=0$

Given planes are $P_1:x-2y+2z+3=0,P_2:3x-6y-2z+2=0$
Here $a_1.a_2+b_1{b}_2+c_1{c}_2>0$

So equation of obtuse angular bisector between the planes $a_{1}x+b_{1}y+c_{1}z+d_1=0,a_{2}x+b_{2}y+c_{2}z+d_2=0$ is given by
$\frac{a_{1}x+b_{1}y+c_{1}z+d_1}{\sqrt{a_1^2+b_1^2+c_1^2}}=\frac{a_{2}x+b_{2}y+c_{2}z+d_2}{\sqrt{a_2^2+b_2^2+c_2^2}}$
$\Rightarrow \frac{x-2y+2z+3}{\sqrt{1+4+4}}=\frac{3x-6y-2z+2}{\sqrt{9+36+4}}$
$\Rightarrow \frac{x-2y+2z+3}{3}=\frac{3x-6y-2z+2}{7}$
$\Rightarrow 2x-4y-20z-15=0$