Question

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

Answer 1

Using the fact that reflection 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)=(a2+b2+c2)(a′x+b′y+c′z+d′)

Given:2x−3y+4z=3 where a′=2,b′=−3,c′=4,d′=−3

x−y+z=3 where a=1,b=−1,c=1,d=−3

Required equation is 2(2+3+4)(x−y+z−3)=(1+1+1)(2x−3y+4z−3)

⇒6(x−y+z−3)=2x−3y+4z−3

Required equation is 2(2+3+4)(x−y+z−3)=(1+1+1)(2x−3y+4z−3)

⇒6(x−y+z−3)=2x−3y+4z−3

⇒4x−3y+2z−15=0