The equation of the plane passing through the point (1,2,2) and perpendicular to the planes x-y+2 z=3 and 2 x -2 y + z +12=0 , is

Step-by-step solution

The equation of plane passing through the point (1,2,2) is a(x-1)+b(y-2)+c(z-2)=0 ...(i) Since eq ^ n (i) is normal to the planes x-y+2 z=3 and 2 x-2 y+z+12=0 a-b+2 c=0 ...(ii) and 2 a-2 b+c=0 ...(iii) From eq ^ n (ii) and (iii) aligned & a -1+4 = -b 1-4 = c -2+2 = (say) & a=3 , b=3 , c=0 aligned Using the above values in eq ^ n (i), we get: aligned & 3 ( x -1)+3 ( y -2)+0( z -2)=0 & x-1+y-2=0 x+y-3=0 aligned