You need an angle between two things. One of them is PQ, and you only need the vector PQ, not the equation of the line. The other thing is the plane. But there isn't a single direction vector for the plane, because it's two-dimensional. However, there is a single vector normal to the plane - do you know how to get this from the equation of the plane?
Once you have vector PQ and the normal vector to the plane, you can use the usual method for the angle between two vectors. But you need to consider how the angle between PQ and the normal is related to the angle between PQ and the plane itself - this may explain why you are asked for the sine of the angle and not the cosine.