Find the equation of the plane passing through the point (1, -2, 7) and parallel to the plane 5x + 4y - 11z = 6.

Let the equation of plane be

Direction ratios of parallel planes are related to each other as

Putting the values from the equation of a given parallel plane,

Putting in the equation of a plane

As the plane is passing through (1,-2,7), it must satisfy the plane,

(1)

Putting value in equation (1), we have

5x + 4y-11z + 80=0

So, the required equation of the plane is 5x + 4y-11z + 80=0.