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.

Question

Philoid · Accepted Answer

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