The equation of the plane passing through the intersection of the planes 2 x+y+2 z=9,4 x-5 y-4 z=1 and the point (3,2,1) is

Step-by-step solution

The equation of plane passing through the intersection of planes 2 x+y+2 z=9 and 4 x-5 y-4 z=1 is (2 x+y+2 z-9)+ (4 x-5 y-4 z-1)=0 Given that this plane passes through (3,2,1) aligned & 2(3)+2+2(1)-9+ [4(3)-5(2)-4(1)-1]=0 & 1+ (-3)=0 & = 1 3 aligned Equation is (2 x+y+2 z-9)+ 1 3 (4 x-5 y-4 z-1)=0 aligned & 6 x+3 y+6 z-27+4 x-5 y-4 z-1=0 & 10 x-2 y+2 z-28=0 & 10 x-2 y+2 z=28 aligned