1. The given line has the direction vector

2. Let denote the point in the plane who is situated on the line perpendicular to the given line. Then you know:

3. Plug in the known components:

and yields

4. Choose a suitable value for c. I used c = 1. That means the Point Q is Q(3, -1, 1).

The equation of the line is

5. I attached a sketch: The given line in green, the point P in red, the point Q in yellow and the line PQ in orange.