A line with direction ratios 2,1,2 intersect each of the lines  x=y+a=z and  x+a=2y=2z  the co-ordinates of each of the points of intersection are

The given lines arex1=y+a1=z1,  x+a2=y1=z1Suppose that the line L intersect the above two lines at P,QThe direction rations of PQ are 2,1,2The points   Ps,s−a,sand  Q2t−a,t,t, these are general points on the given two lines. Direction ratios of  PQare  2t−a−s,t−s+a,t−s, these are proportional to 2,1,2It implies that 2t−a−s2=t−s+a1=t−s2Hence, s=3a,t=aTherefore, the points of intersections are   P3a,2a,3a, Qa,a,a