First I don't think that s and t can be constants ,because if it is, there cannot be a line and
Now to the problem,
take the position vector of P and Q are respectively, and
take vectors parallel to and respectively and then,
So let's consider the given fact now, it says the is perpendicular to both and . This means following dot products should be equal to zero.
from these two equation you'll get two equations involving . Solve them and find the position vector of P and Q
you'll eventually get