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

then

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