A line with direction cosines proportional to 1, -5 and-2 meets lines x= y + 5= z + 1 and  x + 5 = 3y=2z.The coordinates of each of the points of the intersection are given by

Let the coordinates of the point(s) be a, b and c. Therefore, the equation of the line passing through (a, b, c) and whose direction ratios are 1, - 5 and-2 is x−a1=y−b−5=z−c−2-----(i)Line (i) intersects the line, x1=y+51=z+11----iiTherefore, these are coplanar. 1−5−2111ab+5c+1=0a+b−2c+3=0Also, by using same procedure with the second equation, we get the condition