If the line x−2−1=y+21=z+k4 is one of the angle  bisectors of the lines x1=y−2=z3 and x−2=y3=z1 then  the value of k is

Since point of intersection of the given lines is (0, 0, 0), it must lie on the angle bisector.  so, 0−2−1=0+21=0+k4⇒ k=8 See the angle between the angular bisectors and the given line must be same