Vector equation of the plane with the point and normal vector is  .

The plane that passes through the point and contains the line of itersection of the planes and .

Here and .

The resulting vector is .

The vector is .

Find the second point line of intersecition substitute in and .

and .

Add the above two equations.

.

Substitute in .

.

The another vector is .

Since and lie in the same plane, the cross product is orthogonal to the that plane and it can be represented as perpendicular vector .

Hence the vector .

Vector equation of the plane with the point and normal vector is

.

Here and .

Substitute above values in vector equation formula.

.

The equation of the plane is .