Two points that lie on the first line are p1 = (14,1,10) and p2 = (4,-1,2) (by inspection)
Also, two points that lie on the second line are p3 = (0,9,5) and p4 = (-5,8,1)
The two lines are parallel if (p1 - p2) is a scalar multiple of (p3 - p4)
p1 - p2 = (10,2,8)
p3 - p4 = (5,1,4)
So...