If 2 mutually perpendicular lines with their direction cosines are given then what will be the direction cosines of the third line which is perpendicular to both the given lines

let the two lines be ax + by + cz = d kx + ly + mz = n where a,b,c and k,l,m are the direction cosines of the two lines. the vectors parallel to the two lines are ai + bj + ck and ki + lj + mk now find the cross product of the two vectors to find the vector perpendicular to the them . let the cross product be Ai + Bj + Ck so the DCs of the line perpendicular to both the given lines is A/(A^2 + B^2 + C^2)^1/2 , B/(A^2 + B^2 + C^2)^1/2 , C/(A^2 + B^2 + C^2)^1/2 this question i have solved taking the general ref . it doesn't matter whether the given lines are perpendicular or not.