Find the equation of the plane passing through the point A(-1, -1, 2) and perpendicular to each of the planes 3x + 2y - 3z = 1 and 5x – 4y + z = 5.

Applying the condition of perpendicularity between planes

Where A, B, C are direction ratios of plane and A₁, B₁, C₁ are of another plane.

(1)

(2)

And plane passes through (-1,-1,2),

A(x + 1) + B(y + 1) + C(z-2)=0 (3)

On solving equation (1) and (2)

Putting values in equation (3)

B(5x + 5 + 9y + 9 + 11z-22)=0

5x + 9y + 11z-8=0

So, required equation of plane is 5x + 9y + 11z=8.