JEE Main 2021 (Online) 27th July Morning ShiftQuestion 1
Let the plane passing through the point $(-1,0,-2)$ and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to :
3D Geometry
Solution
Normal $=(2,1,-1)\times(1,-1,-1)=(-2,1,-3)$. Plane through $(-1,0,-2)$: $-2(x+1)+y-3(z+2)=0\Rightarrow -2x+y-3z-8=0\Rightarrow 2x-y+3z+8=0$. $a+b+c=2-1+3=4$. Option (C).