1. There doesn't exist only one vector parallel to the given plane but an unlimited number of parallel vectors.

2. To find one of them it is sufficient to calculate the coordinates of two points in the plane which determine a vector which is parallel to the plane.

3. As an example: and determine a vector .

For further calculations use

4. From the wording of the question I assume that you are asked to determine the equation of a line passing through the given point and parallel to the plane. If so:

But, as I#ve mentioned above, there are an unlimited number of such lines, which are situated in a plane parallel to the given plane.