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.

Question

Philoid · Accepted Answer

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