The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2 x-y-2 z=5$ and $3 x-6 y+2 z=7$ is

Question

Aicharya · Accepted Answer

Required plane is perpendicular to planes $2 x-y-2 z=5$ and $3 x-6 y+2 z=7$ Equation of required plane is $\begin{aligned} & \left|\begin{array}{ccc} x-1 & y-1 & z-1 \ 2 & -1 & -2 \ 3 & -6 & 2 \end{array}ight|=0 \ & \Rightarrow(x-1)(-14) \div(y-1)(10) \ & \quad+(z-1)(-12+3)=0 \ & \Rightarrow-14 x+14-10 y+10-9 z+9=0 \ & \Rightarrow 14 x+10 y+9 z=-33 \end{aligned}$

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2 x-y-2 z=5$…

Solution