Find the equation of the plane passing through the points A(-1, 1, 1) and B(1, -1, 1) and perpendicular to the plane x + 2y + 2z = 5.
Plane passes through (-1,1,1) and (1,-1,1),
A(x + 1) + B(y-1) + C(z-1)=0 (1)
A(x-1) + B(y + 1) + C(z-1)=0 (2)
Subtracting (1) from (2),
A(x-1-x-1) + B(y + 1-y + 1)=0
-2A + 2B=0
A=B (3)
Now plane is perpendicular to x + 2y + 2z=5
A + 2B + 2C=0 (4)
Using (3) in (4)
B + 2B + 2C=0
3B + 2C=0
Putting values in equation (1)
B(2(x + 1) + 2(y-1)-3(z-1)=0
2x + 2y-3z + 2-2-3=0
2x + 2y-3z-3=0