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

The plane that passes through the point and contains the line with symmentric equations .

Here .

One vector in the plane will be the vector contained in the line , since the line is

contained in the plane, the symmentric equations in the plane can be written as ,

therefore the vector is .

The vector plane is .

The second vector in the plane is vector between and  is .

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