• # question_answer The equation of the plane passing through the points (0, 1, 2) and (?1, 0, 3) and perpendicular to the plane            $2x+3y+z=5$ is [J & K 2005] A)            $3x-4y+18z+32=0$ B)            $3x+4y-18z+32=0$ C)            $4x+3y-17z+31=0$ D)            $4x-3y+z+1=0$

Equation of any plane passing through  (0, 1, 2) is                                 $a(x-0)+b(y-1)+c(z-2)=0$           ......(i)                    Plane (i) passes through (?1, 0, 3), then                                 $a(-1-0)+b(0-1)+c(3-2)=0$                    Þ $-a-b+c=0$Þ $a+b-c=0$                                .....(ii)                    Plane (i) is perpendicular to the plane $2x+3y+z=5$, then $2a+3b+c=0$                                         ......(iii)                    Solving (ii) and (iii), we get $a=-4k,b=3k,c=-k$                    Putting these values in (i),                        $-4k(x)+3k(y-1)-k(z-2)=0$                    Þ $-4x+3y-3-z+2=0$                    Þ $-4x+3y-z-1=0$ Þ $4x-3y+z+1=0$.