A line with direction cosines proportional to 1, -5 and-2 meets lines x = y + 5 = z + 1 and x + 5 = 3y = 2r. 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 isx-a1=y-b-5=z-c-2                      (i)Line (i) intersects the line,x1=y+51=z+11                             (ii)Therefore, these are coplanar.1-5-2111ab+5c+1=0or a + b - 2c + 3 = 0Also, by using same procedure with the second equation, we get the condition11a + 15b - 32c + 55 = 0