use formula for line that goes through 3 points

and to intersect plane at any (let's say your point) line that you get from that up there must have point (P(3,1,-2))

hint: draw it for your self ... it make more sense that way

P.S. actually as i more think of it... this could be some "problem" if there is equation of the plane so you need to find where that line intersects (if intersect) plane ... but this way when you solve that determinant up there there is not much to do ... if you have 3 points there is no another way to draw line through them except like that, and there is no another condition by which you can lean it so it will go through plane at that point ...

funny thing is that you can substitute any from P,Q,R with that P on the plane and put in determinant and you will get the same result