Find the point P on the line L through the points A(5, 1, 7) and B(6, 0, 8) and the point Q on the line M through the points C(3, 1, 3) and D(–1, 3, 3) such that the line through P and Q is perpendicular to both lines L and M. Verify that P and Q are at a distance √6 apart, and find the point where the line through P and Q intersects the coordinate plane Oxy.