Find the equation of the plane passing through the points A(1,-1,2) and B(2,-2,2) and perpendicular to the plane `6x-2y+2z=9`.
Plane passes through (1,1,2) and (2,- 2,2),
A(x – 1) + B(y -1) + C(z – 2) = 0 (1)
A(x – 2) + B(y + 2) + C(z – 2) = 0 (2)
Subtracting (1) from (2),
A(x – 2 – x + 1) + B(y + 2 – y-1) = 0
A – 3B = 0 (3)
Now plane is perpendicular to
6x – 2y + 2z = 9 6A – 2B + 2C = 0 (4)
Using (3) in (4)
18A – 2B + 2C = 0
16B + 2C = 0
C = – 8B
Putting values in equation (1)
3B(x – 1) + B(y + 2) – 8B(z – 2) = 0
B(3x – 3 + y + 2 – 8z + 16) = 0
3x + y – 8z + 15 = 0
Correct Answer – `x+y-2z+4=0`